动量守恒定律
Created: 2025-08-20 09:44:55
Explain the Pythagorean Theorem
Created: 2025-08-20 11:05:52
太阳系运动
Created: 2025-08-24 07:37:17
在Java中什么是零拷贝
Created: 2025-08-24 07:55:07
如何绘制路易斯结构
Created: 2025-08-24 08:03:05
什么是SVG
Created: 2025-08-24 08:12:32
在Java中什么是泛型
Created: 2025-08-24 08:34:34
什么是黎曼函数
Created: 2025-08-24 08:46:29
Explain the Pythagorean Theorem
Created: 2025-08-25 20:50:21
Explain Properties of Kites
Created: 2025-08-25 20:53:22
Explain Euler's formula
Created: 2025-08-25 20:56:28
Explain Laws of Exponents
Created: 2025-08-25 21:00:15
Explain One-to-one function
Created: 2025-08-25 21:03:43
Explain Inverse function
Created: 2025-08-25 21:06:59
Explain the Remainder theorem
Created: 2025-08-25 21:10:10
Explain Rational Zero Theorem
Created: 2025-08-25 21:13:22
Explain Product-to-sum formula
Created: 2025-08-25 21:16:13
Explain Heron's formula
Created: 2025-08-25 21:20:02
Explain De Moivre's Theorem
Created: 2025-08-25 21:23:16
Explain Cramer's Rule
Created: 2025-08-25 21:26:37
Explain Angle of rotation
Created: 2025-08-25 21:29:59
Explain Similar Triangles Theorem
Created: 2025-08-25 21:33:01
Explain Congruent Triangles Theorem
Created: 2025-08-25 21:37:53
Explain Geometric Sequence
Created: 2025-08-25 21:43:28
Explain Arithmetic Sequence
Created: 2025-08-25 21:46:41
Explain Permutation
Created: 2025-08-25 21:49:23
Explain Directrix
Created: 2025-08-25 21:51:42
Explain Eccentricity
Created: 2025-08-25 21:54:07
Explain Ohm's Law
Created: 2025-08-25 21:56:30
Explain Newton's First Law of Motion
Created: 2025-08-25 21:58:35
Explain Newton's Second Law of Motion
Created: 2025-08-25 22:00:49
Explain Hooke's law
Created: 2025-08-25 22:03:02
Explain Gravitational Force
Created: 2025-08-25 22:06:32
Explain Centrifugal force
Created: 2025-08-25 22:09:07
Explain Kinetic energy
Created: 2025-08-25 22:11:38
Explain Torque
Created: 2025-08-25 22:13:50
Explain Right-hand rule
Created: 2025-08-25 22:16:53
Explain Snell's Law
Created: 2025-08-25 22:20:19
Explain The Ideal Gas Law
Created: 2025-08-25 22:22:44
Explain Pascal's Principle
Created: 2025-08-25 22:25:29
Explain Avogadro's number
Created: 2025-08-25 22:28:20
Explain Dalton's law of partial pressures
Created: 2025-08-25 22:31:31
Explain PV diagram
Created: 2025-08-25 22:33:51
Explain Color wavelengths
Created: 2025-08-25 22:36:29
Explain Ultrasound
Created: 2025-08-25 22:39:49
Explain Coulomb's law
Created: 2025-08-25 22:41:50
下降
Created: 2025-08-28 01:57:05
自由落体
Created: 2025-08-28 02:05:25
在java中,什么是volatile
Created: 2025-09-01 06:15:57
If two vectors have the same magnitude, do their components have to be the same?
Created: 2025-09-01 06:28:21
Explain Kirchhoff's voltage law
Created: 2025-09-01 06:43:29
Explain Thévenin's theorem
Created: 2025-09-01 07:26:36
什么是傅里叶变换
Created: 2025-09-01 08:10:47
什么是三角函数
Created: 2025-09-01 08:20:47
netty和smart-socket的区别
Created: 2025-09-01 08:48:51
什么是向量
Created: 2025-09-01 08:52:03
讲一下滑轮常见的中考题型
Created: 2025-09-01 09:09:39
什么是 KNN
Created: 2025-09-01 10:54:00
比特币挖矿
Created: 2025-09-01 11:48:30
种子下载
Created: 2025-09-01 12:29:49
Explain The Pigeonhole Principle
Created: 2025-09-02 00:15:47
Explain De Morgan's Laws
Created: 2025-09-02 00:19:00
Explain The Time Complexity of Linear Search
Created: 2025-09-02 00:22:02
Explain The Properties of a Binary Tree
Created: 2025-09-02 00:24:39
Explain The Triangle Inequality Theorem
Created: 2025-09-02 00:26:32
Explain Hamming distance
Created: 2025-09-02 00:29:58
Explain Big O notation
Created: 2025-09-02 00:32:18
Explain Deadlock
Created: 2025-09-02 00:35:07
Explain Bubble Sort
Created: 2025-09-02 00:37:52
Explain Karnaugh Map
Created: 2025-09-02 00:43:30
Explain Hash table
Created: 2025-09-02 00:48:17
Explain Linked list
Created: 2025-09-02 00:53:36
Explain Chain Code
Created: 2025-09-02 00:58:16
Explain Signal-to-noise ratio
Created: 2025-09-02 01:04:14
Explain Run-length encoding
Created: 2025-09-02 01:09:58
Explain Elbow method
Created: 2025-09-02 01:16:03
Explain Huffman coding
Created: 2025-09-02 01:23:05
Explain Paging
Created: 2025-09-02 01:27:31
Explain OSI model
Created: 2025-09-02 01:31:53
Explain IEEE Convertion
Created: 2025-09-02 01:34:50
Explain The Aufbau Principle
Created: 2025-09-02 01:38:58
Explain The Law of Conservation of Mass
Created: 2025-09-02 01:42:57
Explain The Octet Rule
Created: 2025-09-02 01:47:15
Explain Alkali metals
Created: 2025-09-02 01:51:50
Explain Distillation
Created: 2025-09-02 01:56:44
i want you to teach a 2rd grade math for additions and subtractions
Created: 2025-09-02 01:57:28
Explain Crystallization
Created: 2025-09-02 02:01:00
Explain Titration
Created: 2025-09-02 02:04:42
Explain Ionic Compound
Created: 2025-09-02 02:08:48
Explain Noble gas
Created: 2025-09-02 02:13:22
Explain Transition Metal
Created: 2025-09-02 02:17:41
Explain Balance Chemical Equation
Created: 2025-09-02 02:21:46
Explain Combustion analysis
Created: 2025-09-02 02:26:34
Explain Oxidation
Created: 2025-09-02 02:30:39
Explain First law of thermodynamics
Created: 2025-09-02 02:34:32
Explain Hess's Law
Created: 2025-09-02 02:38:17
Explain Charles's Law
Created: 2025-09-02 02:41:41
Explain Gay-Lussac's Law
Created: 2025-09-02 02:44:21
Explain pH Scale Definition
Created: 2025-09-02 02:48:21
Explain Van't Hoff Equation
Created: 2025-09-02 02:52:20
Explain The Factor Theorem
Created: 2025-09-02 02:55:18
Explain The Law of Sines
Created: 2025-09-02 02:58:47
Explain The Binomial Theorem
Created: 2025-09-02 03:01:33
Explain The Intermediate Value Theorem
Created: 2025-09-02 03:04:56
Explain The Cosine Rule
Created: 2025-09-02 03:07:48
Explain The Divergence Test
Created: 2025-09-02 03:10:31
Explain The Squeeze Theorem (or Sandwich Theorem)
Created: 2025-09-02 03:14:29
Explain The Chain Rule
Created: 2025-09-02 03:17:07
Explain Product Rule
Created: 2025-09-02 03:19:22
Explain Quotient Rule
Created: 2025-09-02 03:22:05
Explain Power Rule
Created: 2025-09-02 03:25:02
Explain Integration by Substitution
Created: 2025-09-02 03:27:04
Explain Disk & Washer Method
Created: 2025-09-02 03:30:04
Explain Extreme value theorem
Created: 2025-09-02 03:32:50
Explain Fermat's theorem
Created: 2025-09-02 03:35:22
Explain Mean Value Theorem
Created: 2025-09-02 03:37:27
Explain Newton-Raphson method
Created: 2025-09-02 03:40:31
Explain Rolle's theorem
Created: 2025-09-02 03:42:57
Explain Second derivative test
Created: 2025-09-02 03:45:42
Vue3
Created: 2025-09-02 03:47:23
Explain Pappus's Theorem
Created: 2025-09-02 03:48:34
Explain The Work-Energy Theorem
Created: 2025-09-02 03:51:35
Explain The Law of Conservation of Energy
Created: 2025-09-02 03:54:27
Explain The Law of Universal Gravitation
Created: 2025-09-02 03:57:07
Explain Archimedes' Principle
Created: 2025-09-02 03:59:33
Explain The Doppler Effect
Created: 2025-09-02 04:01:34
Explain The Principle of Superposition of Waves
Created: 2025-09-02 04:03:43
Explain Kepler's laws of planetary motion
Created: 2025-09-02 04:06:00
Explain Gauss's law
Created: 2025-09-02 04:07:49
Explain Stokes' law
Created: 2025-09-02 04:10:03
Explain Bernoulli's principle
Created: 2025-09-02 04:11:55
Explain Poiseuille's law
Created: 2025-09-02 04:14:12
Explain Stefan-Boltzmann Law of Radiation
Created: 2025-09-02 04:16:52
Explain Carnot cycle
Created: 2025-09-02 04:18:44
Explain Electromagnetic spectrum
Created: 2025-09-02 04:20:46
Explain Ampere's law
Created: 2025-09-02 04:23:14
Explain Brewster's law
Created: 2025-09-02 04:25:23
Explain Brownian motion
Created: 2025-09-02 04:27:39
Explain Hubble's law
Created: 2025-09-02 04:29:40
Explain Tsiolkovsky rocket equation
Created: 2025-09-02 04:31:31
Explain Hall Effect
Created: 2025-09-02 04:33:36
Explain The Halting Problem (Undecidability)
Created: 2025-09-02 04:36:21
Explain The Time Complexity of Binary Search
Created: 2025-09-02 04:38:42
Explain The Correctness of Simple Sorting Algorithm (e.g. Bubble Sort)
Created: 2025-09-02 04:40:59
Explain The Church-Turing Thesis
Created: 2025-09-02 04:43:42
Explain The Relationship between Recursion and Induction
Created: 2025-09-02 04:46:06
Explain Chroma Subsampling
Created: 2025-09-02 04:50:06
Explain Median filtering
Created: 2025-09-02 04:53:03
Explain Shannon Lower bound
Created: 2025-09-02 04:55:54
Explain Dijkstra's algorithm
Created: 2025-09-02 04:59:30
Explain K-means clustering
Created: 2025-09-02 05:02:38
Explain K-nearest neighbors
Created: 2025-09-02 05:07:08
Explain Gradient descent
Created: 2025-09-02 05:11:23
Explain Markov Decision Processes
Created: 2025-09-02 05:16:01
Explain ALOHA network
Created: 2025-09-02 05:20:31
Explain Discrete Cosine Transform
Created: 2025-09-02 05:24:42
Explain Master Theorem
Created: 2025-09-02 05:28:42
Explain Fast Fourier Transform
Created: 2025-09-02 05:31:45
Explain SR latch
Created: 2025-09-02 05:52:30
Explain TCP Reno
Created: 2025-09-02 05:56:56
Explain Chord P2P Network and finger table
Created: 2025-09-02 06:00:30
Explain Le Chatelier's Principle
Created: 2025-09-02 06:04:20
Explain The Pauli Exclusion Principle
Created: 2025-09-02 06:07:45
Explain Raoult's Law
Created: 2025-09-02 06:11:11
find all (x,y) of horiz and vert, tangency. x=7 cos(t) ; y=7 sin(t) 讲解一下这道题目
Created: 2025-09-02 06:13:44
Explain Beer-Lambert Law
Created: 2025-09-02 06:15:25
Explain Phase diagram
Created: 2025-09-02 06:18:07
Explain Boyle's Law
Created: 2025-09-02 06:21:00
Explain Graham's Law of Effusion
Created: 2025-09-02 06:24:17
Explain Arrhenius Equation
Created: 2025-09-02 06:27:19
Explain Henry's law
Created: 2025-09-02 06:30:50
Explain Lewis Acid-Base Theory
Created: 2025-09-02 06:35:59
Explain Clausius-Clapeyron Equation
Created: 2025-09-02 06:39:04
Explain Michaelis-Menten Kinetics
Created: 2025-09-02 06:42:31
Explain Gibbs Free Energy Equation
Created: 2025-09-02 06:46:17
Explain Transition State Theory
Created: 2025-09-02 06:49:25
Explain Koopman's Theorem
Created: 2025-09-02 06:52:52
对于参数方程，切线的斜率可以用导数来表示。具体来说，dy/dx = (dy/dt)/(dx/dt)。当 dy/dx = 0 时，切线是水平的；当 dy/dx 不存在（即 dx/dt = 0 而 dy/dt ≠ 0）时，切线是垂直的。
Created: 2025-09-02 06:55:00
Explain Recrystallization
Created: 2025-09-02 06:56:00
什么是导数,如何求导数
Created: 2025-09-02 06:57:14
Explain Electrogravimetry
Created: 2025-09-02 07:00:02
Explain Kjeldahl Method
Created: 2025-09-02 07:02:51
Explain Liquid-Liquid Extraction
Created: 2025-09-02 07:06:13
Explain Reflux
Created: 2025-09-02 07:09:14
Explain Taylor's theorem
Created: 2025-09-02 07:12:13
Explain Simpson's rule
Created: 2025-09-02 07:15:22
Explain Velocity vector
Created: 2025-09-02 07:19:14
Explain Double Riemann sum
Created: 2025-09-02 07:24:24
Explain Fubini's theorem
Created: 2025-09-02 07:28:11
Explain Jacobian matrix and determinant
Created: 2025-09-02 07:32:43
Explain Green's theorem
Created: 2025-09-02 07:36:11
Explain Stokes' theorem
Created: 2025-09-02 07:40:07
Explain Burnside's Lemma
Created: 2025-09-02 07:45:01
Explain Lah Number
Created: 2025-09-02 07:48:13
Explain Ramsey's theorem
Created: 2025-09-02 07:52:04
Explain Schwarz Lemma theorem
Created: 2025-09-02 07:54:52
Explain Cauchy Riemann Theorem
Created: 2025-09-02 07:58:40
Explain Morera's Theorem
Created: 2025-09-02 08:01:37
Explain Catalan-Mingantu Number
Created: 2025-09-02 08:04:38
Explain Liouville's theorem
Created: 2025-09-02 08:07:47
Explain Derangement Formula
Created: 2025-09-02 08:12:12
Explain Delian problem
Created: 2025-09-02 08:40:20
Explain Polya's Enumeration Theorem
Created: 2025-09-02 08:43:22
Explain Cauchy's theorem
Created: 2025-09-02 08:45:53
Explain Boltzmann machine
Created: 2025-09-02 08:48:35
Explain Geometric Brownian Motion
Created: 2025-09-02 08:51:43
Explain Fermat's Principle
Created: 2025-09-02 08:54:56
Explain Huygens's Principle
Created: 2025-09-02 08:58:28
Explain Virial Theorem
Created: 2025-09-02 09:00:53
Explain Poynting Theorem
Created: 2025-09-02 09:03:44
Explain Fresnel transmission equations
Created: 2025-09-02 09:06:29
Explain Fourier Heat Conduction Law
Created: 2025-09-02 09:09:17
Explain Ampère's circuital law
Created: 2025-09-02 09:12:25
Explain Malus's Law
Created: 2025-09-02 09:15:41
Explain Van der Waals Equation
Created: 2025-09-02 09:18:22
Explain Rayleigh Criterion
Created: 2025-09-02 09:20:59
Explain Paschen Curve
Created: 2025-09-02 09:23:13
Explain Chandrasekhar Limit
Created: 2025-09-02 09:25:39
Explain Landau Damping
Created: 2025-09-02 09:28:43
Explain Schwarzschild radius
Created: 2025-09-02 09:31:07
Explain Babinet's Principle
Created: 2025-09-02 09:33:27
Explain Schrödinger's Cat
Created: 2025-09-02 09:35:36
Explain Rayleigh Criterion for Resolution
Created: 2025-09-02 09:37:37
Explain Navier-Stokes Equations
Created: 2025-09-02 09:40:29
什么是导数
Created: 2025-09-02 09:40:21
Explain Evidence lower bound
Created: 2025-09-02 09:43:45
Explain Viterbi Algorithm
Created: 2025-09-02 09:47:13
Explain Fano's inequality
Created: 2025-09-02 09:50:04
Explain Message Passing algorithm
Created: 2025-09-02 09:52:40
Explain Maximal Planar Graph
Created: 2025-09-02 09:56:15
Explain Cayley's formula
Created: 2025-09-02 09:59:31
Explain Floyd's Cycle Finding Algorithm
Created: 2025-09-02 10:02:52
Explain Sigma-Delta Modulation
Created: 2025-09-02 10:05:34
Explain Kruskal's algorithm
Created: 2025-09-02 10:07:38
Explain Prim's algorithm
Created: 2025-09-02 10:10:15
Explain Region growing by pixel aggregation
Created: 2025-09-02 10:12:51
Explain Arithmetic coding
Created: 2025-09-02 10:15:11
Explain Expectation–maximization (EM) algorithm
Created: 2025-09-02 10:17:16
Explain Differential entropy
Created: 2025-09-02 10:19:13
Explain Kullback–Leibler divergence
Created: 2025-09-02 10:21:02
Explain Principal component analysis
Created: 2025-09-02 10:23:22
Explain Self-attention
Created: 2025-09-02 10:25:37
Explain Adversarial training
Created: 2025-09-02 10:27:31
Explain Forward-Backward Algorithm
Created: 2025-09-02 10:30:08
Explain Cook-Levin Theorem
Created: 2025-09-02 10:32:20
Explain The Henderson-Hasselbalch Equation
Created: 2025-09-02 10:34:29
Explain Bragg's law
Created: 2025-09-02 10:36:43
Explain Debye-Scherrer Equation
Created: 2025-09-02 10:38:49
Explain Hückel's Rule
Created: 2025-09-02 10:40:57
Explain Hard Acid Soft Base Theory
Created: 2025-09-02 10:43:34
Explain Pauli Exclusion Principle
Created: 2025-09-02 10:45:26
Explain Crystal Field Theory
Created: 2025-09-02 10:48:16
Explain Hohenberg-Kohn theorem
Created: 2025-09-02 10:50:34
Explain Frost–Ebsworth diagram
Created: 2025-09-02 10:53:08
Explain Coulson-Fischer Theorem
Created: 2025-09-02 10:55:44
Explain Frank-Condon Principle
Created: 2025-09-02 10:58:22
Explain Nernst Equation
Created: 2025-09-02 11:02:16
Explain Slater's Rules
Created: 2025-09-02 11:05:41
Explain Langmuir Adsorption Isotherm
Created: 2025-09-02 11:08:32
Explain Marcus Theory
Created: 2025-09-02 11:12:07
Explain Eyring Equation
Created: 2025-09-02 11:15:17
Explain Woodward-Hoffmann Rules
Created: 2025-09-02 11:18:53
Explain Born-Haber Cycle
Created: 2025-09-02 11:21:41
Explain Molecular Orbital Theory
Created: 2025-09-02 11:25:03
Explain Hammond Postulate
Created: 2025-09-02 11:27:40
解释勾股定理
Created: 2025-09-02 18:06:08
解释风筝四边形的性质
Created: 2025-09-02 18:07:39
解释欧拉公式
Created: 2025-09-02 18:09:58
解释指数定律
Created: 2025-09-02 18:12:08
解释一对一函数
Created: 2025-09-02 18:14:03
解释反函数
Created: 2025-09-02 18:16:38
解释余数定理
Created: 2025-09-02 18:18:36
解释有理根定理
Created: 2025-09-02 18:20:19
解释积化和公式
Created: 2025-09-02 18:21:47
解释海伦公式
Created: 2025-09-02 18:23:34
解释德莫阿弗定理
Created: 2025-09-02 18:25:20
解释克莱姆法则
Created: 2025-09-02 18:27:42
解释旋转角
Created: 2025-09-02 18:30:05
解释相似三角形定理
Created: 2025-09-02 18:32:12
解释全等三角形定理
Created: 2025-09-02 18:34:17
解释等比数列
Created: 2025-09-02 18:36:29
解释等差数列
Created: 2025-09-02 18:38:11
解释排列
Created: 2025-09-02 18:40:19
解释准线
Created: 2025-09-02 18:42:12
解释偏心率
Created: 2025-09-02 18:44:19
解释欧姆定律
Created: 2025-09-02 18:46:26
解释牛顿第一运动定律
Created: 2025-09-02 18:48:03
解释牛顿第二运动定律
Created: 2025-09-02 18:49:40
解释胡克定律
Created: 2025-09-02 18:51:39
解释引力
Created: 2025-09-02 18:53:29
解释离心力
Created: 2025-09-02 18:55:08
解释动能
Created: 2025-09-02 18:57:16
解释力矩
Created: 2025-09-02 18:59:19
解释右手定则
Created: 2025-09-02 19:00:52
解释斯涅尔定律
Created: 2025-09-02 19:03:13
解释理想气体状态方程
Created: 2025-09-02 19:05:22
解释帕斯卡原理
Created: 2025-09-02 19:07:35
解释阿伏伽德罗常数
Created: 2025-09-02 19:09:39
解释道尔顿分压定律
Created: 2025-09-02 19:11:32
解释压力–体积图
Created: 2025-09-02 19:13:25
解释颜色波长
Created: 2025-09-02 19:15:49
解释超声
Created: 2025-09-02 19:17:53
解释库仑定律
Created: 2025-09-02 19:19:59
解释基尔霍夫电压定律
Created: 2025-09-02 19:22:27
解释戴维南定理
Created: 2025-09-02 19:25:00
解释抽屉原理
Created: 2025-09-02 19:27:20
解释德摩根定律
Created: 2025-09-02 19:29:35
解释线性搜索的时间复杂度
Created: 2025-09-02 19:31:27
解释二叉树的性质
Created: 2025-09-02 19:33:37
解释三角不等式
Created: 2025-09-02 19:35:22
解释汉明距离
Created: 2025-09-02 19:37:08
解释大O表示法
Created: 2025-09-02 19:38:57
解释死锁
Created: 2025-09-02 19:41:10
解释冒泡排序
Created: 2025-09-02 19:43:51
解释卡诺图
Created: 2025-09-02 19:46:01
解释哈希表
Created: 2025-09-02 19:48:35
解释链表
Created: 2025-09-02 19:50:50
解释链码
Created: 2025-09-02 19:52:51
解释信噪比
Created: 2025-09-02 19:55:19
解释行程长度编码
Created: 2025-09-02 19:57:16
解释肘部法
Created: 2025-09-02 19:59:07
解释哈夫曼编码
Created: 2025-09-02 20:01:51
解释分页
Created: 2025-09-02 20:04:13
解释OSI模型
Created: 2025-09-02 20:06:42
解释IEEE转换
Created: 2025-09-02 20:08:13
解释奥夫鲍原理
Created: 2025-09-02 20:10:13
解释质量守恒定律
Created: 2025-09-02 20:12:23
解释八电子规则
Created: 2025-09-02 20:15:17
解释碱金属
Created: 2025-09-02 20:18:02
解释蒸馏
Created: 2025-09-02 20:20:09
解释结晶
Created: 2025-09-02 20:22:59
解释滴定
Created: 2025-09-02 20:24:56
解释离子化合物
Created: 2025-09-02 20:26:48
解释稀有气体
Created: 2025-09-02 20:28:54
解释过渡金属
Created: 2025-09-02 20:31:12
解释化学方程式配平
Created: 2025-09-02 20:33:03
解释燃烧分析
Created: 2025-09-02 20:35:41
解释氧化
Created: 2025-09-02 20:37:37
解释热力学第一定律
Created: 2025-09-02 20:39:19
解释赫斯定律
Created: 2025-09-02 20:41:28
解释查理定律
Created: 2025-09-02 20:43:22
解释盖-吕萨克定律
Created: 2025-09-02 20:45:21
解释pH值定义
Created: 2025-09-02 20:47:13
解释范特霍夫方程
Created: 2025-09-02 20:48:57
解释因式定理
Created: 2025-09-02 20:50:47
解释正弦定理
Created: 2025-09-02 20:52:53
解释二项式定理
Created: 2025-09-02 20:54:45
解释介值定理
Created: 2025-09-02 20:56:30
解释余弦定理
Created: 2025-09-02 20:58:51
解释发散判别法
Created: 2025-09-02 21:00:29
解释夹逼定理
Created: 2025-09-02 21:02:31
解释链式法则
Created: 2025-09-02 21:04:52
解释乘积法则
Created: 2025-09-02 21:06:53
解释商法则
Created: 2025-09-02 21:08:48
解释幂法则
Created: 2025-09-02 21:10:24
解释换元积分法
Created: 2025-09-02 21:11:57
解释圆盘法与圆环法
Created: 2025-09-02 21:14:02
解释极值定理
Created: 2025-09-02 21:15:36
解释费马定理
Created: 2025-09-02 21:17:25
解释中值定理
Created: 2025-09-02 21:19:05
解释牛顿-拉弗森方法
Created: 2025-09-02 21:21:05
解释罗尔定理
Created: 2025-09-02 21:23:15
解释二阶导数判别法
Created: 2025-09-02 21:24:58
解释帕普斯定理
Created: 2025-09-02 21:27:03
解释功-能定理
Created: 2025-09-02 21:28:40
解释能量守恒定律
Created: 2025-09-02 21:30:09
解释万有引力定律
Created: 2025-09-02 21:31:51
解释阿基米德原理
Created: 2025-09-02 21:33:45
解释多普勒效应
Created: 2025-09-02 21:35:43
解释波的叠加原理
Created: 2025-09-02 21:37:36
解释开普勒行星运动定律
Created: 2025-09-02 21:39:12
解释高斯定律
Created: 2025-09-02 21:40:57
解释斯托克斯定律
Created: 2025-09-02 21:43:00
解释伯努利原理
Created: 2025-09-02 21:44:42
解释泊肃叶定律
Created: 2025-09-02 21:47:00
解释斯特藩–玻尔兹曼辐射定律
Created: 2025-09-02 21:48:41
解释卡诺循环
Created: 2025-09-02 21:50:44
解释电磁波谱
Created: 2025-09-02 21:52:44
解释安培定律
Created: 2025-09-02 21:54:32
解释布儒斯特定律
Created: 2025-09-02 21:56:39
解释布朗运动
Created: 2025-09-02 21:58:20
解释哈勃定律
Created: 2025-09-02 22:00:06
解释齐奥尔科夫斯基火箭方程
Created: 2025-09-02 22:01:51
解释霍尔效应
Created: 2025-09-02 22:03:16
解释停机问题（不可判定性）
Created: 2025-09-02 22:05:12
解释二分查找的时间复杂度
Created: 2025-09-02 22:07:09
解释简单排序算法（如冒泡排序）的正确性
Created: 2025-09-02 22:08:37
解释丘奇-图灵论题
Created: 2025-09-02 22:10:31
解释递归与归纳法的关系
Created: 2025-09-02 22:12:27
解释色度抽样
Created: 2025-09-02 22:14:26
解释中值滤波
Created: 2025-09-02 22:16:51
解释香农下界
Created: 2025-09-02 22:18:43
解释迪杰斯特拉算法
Created: 2025-09-02 22:20:35
解释K均值聚类
Created: 2025-09-02 22:22:24
解释K近邻算法
Created: 2025-09-02 22:24:17
解释梯度下降
Created: 2025-09-02 22:26:00
解释马尔可夫决策过程
Created: 2025-09-02 22:29:04
解释ALOHA网络
Created: 2025-09-02 22:30:59
解释离散余弦变换
Created: 2025-09-02 22:33:14
解释主定理
Created: 2025-09-02 22:35:15
解释快速傅里叶变换
Created: 2025-09-02 22:37:21
解释SR触发器
Created: 2025-09-02 22:39:57
解释TCP Reno
Created: 2025-09-02 22:42:08
解释Chord P2P网络及指针表
Created: 2025-09-02 22:44:41
解释勒沙特列原理
Created: 2025-09-02 22:46:16
解释泡利不相容原理
Created: 2025-09-02 22:48:34
解释拉乌尔定律
Created: 2025-09-02 22:50:41
解释比尔-朗伯定律
Created: 2025-09-02 22:52:37
解释相图
Created: 2025-09-02 22:54:45
解释玻意耳定律
Created: 2025-09-02 22:56:35
解释格雷厄姆定律
Created: 2025-09-02 22:58:46
解释阿伦尼乌斯方程
Created: 2025-09-02 23:00:39
解释亨利定律
Created: 2025-09-02 23:02:39
解释路易斯酸碱理论
Created: 2025-09-02 23:04:57
解释克劳修斯–克拉佩龙方程
Created: 2025-09-02 23:06:49
解释米氏–门腾动力学
Created: 2025-09-02 23:08:51
解释吉布斯自由能方程
Created: 2025-09-02 23:10:58
解释过渡态理论
Created: 2025-09-02 23:12:23
解释库普曼定理
Created: 2025-09-02 23:14:17
解释重结晶
Created: 2025-09-02 23:16:02
解释电重力测定法
Created: 2025-09-02 23:18:12
解释凯氏定氮法
Created: 2025-09-02 23:20:08
解释液-液萃取
Created: 2025-09-02 23:22:07
解释回流
Created: 2025-09-02 23:24:35
解释泰勒定理
Created: 2025-09-02 23:26:00
解释辛普森法则
Created: 2025-09-02 23:27:47
解释速度矢量
Created: 2025-09-02 23:29:20
解释二重黎曼和
Created: 2025-09-02 23:32:08
解释富比尼定理
Created: 2025-09-02 23:34:01
解释雅可比矩阵及行列式
Created: 2025-09-02 23:36:10
解释格林定理
Created: 2025-09-02 23:37:51
解释斯托克斯定理
Created: 2025-09-02 23:39:56
解释伯恩赛德引理
Created: 2025-09-02 23:41:52
解释Lah数
Created: 2025-09-02 23:43:50
解释拉姆齐定理
Created: 2025-09-02 23:45:46
解释施瓦茨引理
Created: 2025-09-02 23:47:48
解释柯西-黎曼定理
Created: 2025-09-02 23:49:27
解释莫雷拉定理
Created: 2025-09-02 23:51:03
解释Catalan-Mingantu数
Created: 2025-09-02 23:52:40
解释刘维尔定理
Created: 2025-09-02 23:54:23
解释错排公式
Created: 2025-09-02 23:56:40
解释狄利安问题
Created: 2025-09-02 23:58:38
解释宝莱枚举定理
Created: 2025-09-03 00:00:22
解释柯西定理
Created: 2025-09-03 00:02:15
解释玻尔兹曼机
Created: 2025-09-03 00:04:27
解释几何布朗运动
Created: 2025-09-03 00:05:53
解释费马原理
Created: 2025-09-03 00:07:54
解释惠更斯原理
Created: 2025-09-03 00:10:11
解释维里定理
Created: 2025-09-03 00:12:07
解释坡印廷定理
Created: 2025-09-03 00:14:21
解释菲涅尔透射方程
Created: 2025-09-03 00:16:19
解释傅里叶热传导定律
Created: 2025-09-03 00:18:22
解释安培环路定律
Created: 2025-09-03 00:20:56
解释马吕斯定律
Created: 2025-09-03 00:23:12
解释范德瓦尔斯方程
Created: 2025-09-03 00:25:16
解释瑞利判据
Created: 2025-09-03 00:27:36
解释帕申曲线
Created: 2025-09-03 00:29:25
解释钱德拉塞卡极限
Created: 2025-09-03 00:31:53
解释朗道阻尼
Created: 2025-09-03 00:34:37
解释施瓦茨希尔德半径
Created: 2025-09-03 00:36:52
解释巴比奈原理
Created: 2025-09-03 00:39:32
解释薛定谔的猫
Created: 2025-09-03 00:42:07
解释分辨率的瑞利判据
Created: 2025-09-03 00:44:59
解释纳维–斯托克斯方程
Created: 2025-09-03 00:48:27
解释证据下界
Created: 2025-09-03 00:51:29
解释维特比算法
Created: 2025-09-03 00:56:25
解释法诺不等式
Created: 2025-09-03 01:00:38
解释消息传递算法
Created: 2025-09-03 01:04:34
解释极大平面图
Created: 2025-09-03 01:08:12
解释凯莱公式
Created: 2025-09-03 01:13:41
解释弗洛伊德环检测算法
Created: 2025-09-03 01:18:32
解释Σ-Δ调制
Created: 2025-09-03 01:22:46
解释克鲁斯卡尔算法
Created: 2025-09-03 01:26:54
解释普里姆算法
Created: 2025-09-03 01:30:11
解释基于像素聚合的区域生长
Created: 2025-09-03 01:33:12
解释算术编码
Created: 2025-09-03 01:36:09
解释期望最大化（EM）算法
Created: 2025-09-03 01:39:21
解释微分熵
Created: 2025-09-03 01:42:06
解释Kullback–Leibler散度
Created: 2025-09-03 01:45:49
解释主成分分析
Created: 2025-09-03 01:48:52
解释自注意力机制
Created: 2025-09-03 01:53:15
解释对抗训练
Created: 2025-09-03 01:56:09
解释前向–后向算法
Created: 2025-09-03 01:59:20
解释库克–列文定理
Created: 2025-09-03 02:02:32
解释亨德森–哈塞尔巴赫方程
Created: 2025-09-03 02:07:53
解释布拉格定律
Created: 2025-09-03 02:10:51
解释德拜–谢勒方程
Created: 2025-09-03 02:14:01
解释休克尔规则
Created: 2025-09-03 02:16:42
解释硬酸–软碱理论
Created: 2025-09-03 02:21:13
解释晶体场理论
Created: 2025-09-03 02:24:13
解释霍恩伯格–科恩定理
Created: 2025-09-03 02:26:13
解释Frost–Ebsworth图
Created: 2025-09-03 02:28:51
解释柯尔森–费舍尔定理
Created: 2025-09-03 02:31:30
解释弗兰克–康登原理
Created: 2025-09-03 02:34:03
解释能斯特方程
Created: 2025-09-03 02:36:52
解释斯莱特规则
Created: 2025-09-03 02:40:22
解释朗缪尔吸附等温线
Created: 2025-09-03 02:43:53
解释马库斯理论
Created: 2025-09-03 02:47:46
解释艾林方程
Created: 2025-09-03 02:50:49
解释伍德沃德–霍夫曼规则
Created: 2025-09-03 02:53:34
解释玻恩–哈伯循环
Created: 2025-09-03 02:56:42
解释分子轨道理论
Created: 2025-09-03 03:00:07
解释哈蒙德假说
Created: 2025-09-03 03:04:07
奇异值分解
Created: 2025-09-03 08:06:02
为什么天空是蓝色?
Created: 2025-09-04 23:04:05
什么是导数
Created: 2025-09-05 01:02:12
圆
Created: 2025-09-05 01:01:57
烟幕干扰弹主要通过化学燃烧或爆炸分散形成烟幕或气溶胶云团，在目标前方特定空域 形成遮蔽，干扰敌方导弹，具有成本低、效费比高等优点。随着烟幕干扰技术的不断发展， 现已有多种投放方式完成烟幕干扰弹的定点精确抛撒，即在抛撒前能精确控制烟幕干扰弹到 达预定位置，通过时间引信时序控制起爆时间。 现考虑运用无人机完成烟幕干扰弹的投放策略问题。具有长续航能力的无人机挂载某型 烟幕干扰弹在特定空域巡飞，受领任务后，无人机投放烟幕干扰弹在来袭武器和保护目标之 间形成烟幕遮蔽。每架无人机投放两枚烟幕干扰弹至少间隔1 s。烟幕干扰弹脱离无人机后， 在重力作用下运动。烟幕干扰弹起爆后瞬时形成球状烟幕云团，由于采用特定技术，该烟幕 云团以3 m/s的速度匀速下沉。据试验数据知，云团中心10 m范围内的烟幕浓度在起爆20 s 内可为目标提供有效遮蔽。 来袭武器为空地导弹，该型导弹飞行速度300 m/s。导弹的飞行方向直指一个为掩护某 半径7 m、高10 m的圆柱形固定目标而专门设置的假目标。以假目标为原点，水平面为 𝑥𝑦 平面，真目标下底面的圆心为 (0,200,0)。警戒雷达发现来袭导弹时，3 枚导弹 M1、M2、 M3分别位于 (20000,0,2000)、(19000,600,2100)、(18000,−600,1900)；5 架无人机的位 置信息分别为 FY1(17800,0,1800)、FY2(12000,1400,1400)、FY3(6000,−3000,700)、 FY4(11000,2000,1800)、FY5(13000,−2000,1300)。 在导弹来袭过程中，通过投放烟幕干扰弹尽量避免来袭导弹发现真目标。控制中心在警 戒雷达发现目标时，立即向无人机指派任务。无人机受领任务后，可根据需要瞬时调整飞行 方向，然后以70~140 m/s的速度等高度匀速直线飞行。每架无人机的航向、速度可不相同， 但一旦确定就不再调整。 为实现更为有效的烟幕干扰效果，需设计烟幕干扰弹的投放策略，主要包括无人机飞行 方向、飞行速度、烟幕干扰弹投放点、烟幕干扰弹起爆点等。请建立数学模型，针对不同情 形，分别设计烟幕干扰弹的投放策略，使得多枚烟幕干扰弹对真目标的有效遮蔽时间尽可能 长。不同烟幕干扰弹的遮蔽可不连续。 问题1 利用无人机FY1投放1枚烟幕干扰弹实施对M1的干扰，若FY1以120 m/s的 速度朝向假目标方向飞行，受领任务1.5 s后即投放1枚烟幕干扰弹，间隔3.6 s后起爆。请 给出烟幕干扰弹对M1的有效遮蔽时长。
Created: 2025-09-05 01:23:43
烟幕干扰弹主要通过化学燃烧或爆炸分散形成烟幕或气溶胶云团，在目标前方特定空域 形成遮蔽，干扰敌方导弹，具有成本低、效费比高等优点。随着烟幕干扰技术的不断发展， 现已有多种投放方式完成烟幕干扰弹的定点精确抛撒，即在抛撒前能精确控制烟幕干扰弹到 达预定位置，通过时间引信时序控制起爆时间。 现考虑运用无人机完成烟幕干扰弹的投放策略问题。具有长续航能力的无人机挂载某型 烟幕干扰弹在特定空域巡飞，受领任务后，无人机投放烟幕干扰弹在来袭武器和保护目标之 间形成烟幕遮蔽。每架无人机投放两枚烟幕干扰弹至少间隔1 s。烟幕干扰弹脱离无人机后， 在重力作用下运动。烟幕干扰弹起爆后瞬时形成球状烟幕云团，由于采用特定技术，该烟幕 云团以3 m/s的速度匀速下沉。据试验数据知，云团中心10 m范围内的烟幕浓度在起爆20 s 内可为目标提供有效遮蔽。 来袭武器为空地导弹，该型导弹飞行速度300 m/s。导弹的飞行方向直指一个为掩护某 半径7 m、高10 m的圆柱形固定目标而专门设置的假目标。以假目标为原点，水平面为 𝑥𝑦 平面，真目标下底面的圆心为 (0,200,0)。警戒雷达发现来袭导弹时，3 枚导弹 M1、M2、 M3分别位于 (20000,0,2000)、(19000,600,2100)、(18000,−600,1900)；5 架无人机的位 置信息分别为 FY1(17800,0,1800)、FY2(12000,1400,1400)、FY3(6000,−3000,700)、 FY4(11000,2000,1800)、FY5(13000,−2000,1300)。 在导弹来袭过程中，通过投放烟幕干扰弹尽量避免来袭导弹发现真目标。控制中心在警 戒雷达发现目标时，立即向无人机指派任务。无人机受领任务后，可根据需要瞬时调整飞行 方向，然后以70~140 m/s的速度等高度匀速直线飞行。每架无人机的航向、速度可不相同， 但一旦确定就不再调整。 为实现更为有效的烟幕干扰效果，需设计烟幕干扰弹的投放策略，主要包括无人机飞行 方向、飞行速度、烟幕干扰弹投放点、烟幕干扰弹起爆点等。请建立数学模型，针对不同情 形，分别设计烟幕干扰弹的投放策略，使得多枚烟幕干扰弹对真目标的有效遮蔽时间尽可能 长。不同烟幕干扰弹的遮蔽可不连续。 问题1 利用无人机FY1投放1枚烟幕干扰弹实施对M1的干扰，若FY1以120 m/s的 速度朝向假目标方向飞行，受领任务1.5 s后即投放1枚烟幕干扰弹，间隔3.6 s后起爆。请 给出烟幕干扰弹对M1的有效遮蔽时长。
Created: 2025-09-05 01:24:52
英语知识体系
Created: 2025-09-05 02:03:02
数学知识体系
Created: 2025-09-05 02:10:28
Count these objects and write the number: ⚽⚽
Created: 2025-09-05 05:54:38
Start at 11 and count forward to 21. Write the numbers
Created: 2025-09-05 06:18:39
Draw a rectangle and a triangle. Label each?
Created: 2025-09-05 06:21:10
"Which is longer
Created: 2025-09-05 06:24:33
Show a way to make 10 using two numbers
Created: 2025-09-05 06:27:07
"Circle the number that is greater
Created: 2025-09-05 06:29:41
How many sides does a square have?
Created: 2025-09-05 06:32:03
"Add within 10
Created: 2025-09-05 06:35:09
"Subtract within 10
Created: 2025-09-05 06:37:43
"Which shape is a solid
Created: 2025-09-05 06:40:17
What is 10 + 5?
Created: 2025-09-05 06:42:34
What is 18 - 9?
Created: 2025-09-05 06:45:04
Count by 10s from 30 to 100
Created: 2025-09-05 06:48:05
Write the value of the digit 7 in 170?
Created: 2025-09-05 06:50:53
"Which is heavier
Created: 2025-09-05 06:53:28
Draw a rectangle and divide it into 2 equal parts. Shade one half?
Created: 2025-09-05 06:55:47
"Which number is greater
Created: 2025-09-05 06:58:15
What time is shown on a clock with the hour hand at 3 and the minute hand at 12?
Created: 2025-09-05 07:00:52
What is 18 + 11?
Created: 2025-09-05 07:04:13
Count by 10s from 20 to 100
Created: 2025-09-05 07:06:54
Write the value of the digit 7 in 70?
Created: 2025-09-05 07:09:37
What is 200 + 140?
Created: 2025-09-05 07:11:37
What is 705 - 268?
Created: 2025-09-05 07:13:09
How many quarters make $1.50?
Created: 2025-09-05 07:15:29
A rectangle has sides 9 cm and 8 cm. What is the perimeter
Created: 2025-09-05 07:17:22
What time is 15 minutes after 1:30?
Created: 2025-09-05 07:19:45
Write the number that is 10 more than 245?
Created: 2025-09-05 07:22:46
Draw an array with 2 rows of 5 to show repeated addition?
Created: 2025-09-05 07:25:10
Measure a pencil to the nearest inch. Is it 5 inches
Created: 2025-09-05 07:28:04
"Compare using >
Created: 2025-09-05 07:30:27
Round 499 to the nearest ten?
Created: 2025-09-05 07:33:07
What is 300 + 210?
Created: 2025-09-05 07:35:10
What is 755 - 298?
Created: 2025-09-05 07:37:38
A rectangle has sides 9 cm and 6 cm. What is the perimeter
Created: 2025-09-05 07:39:45
Write the number that is 10 more than 512?
Created: 2025-09-05 07:42:23
Draw an array with 3 rows of 3 to show repeated addition?
Created: 2025-09-05 07:44:57
Measure a pencil to the nearest inch. Is it 7 inches
Created: 2025-09-05 07:47:55
Round 351 to the nearest ten?
Created: 2025-09-05 07:50:01
What is 8 x 4?
Created: 2025-09-05 07:53:04
What is 56 ÷ 9?
Created: 2025-09-05 07:55:11
Place 3/4 and 2/3 on a number line from 0 to 1. Which is greater
Created: 2025-09-05 07:58:14
A rectangle is 8 m by 7 m. What is the area
Created: 2025-09-05 08:00:43
A movie starts at 3:10 PM and ends at 4:45 PM. How many minutes long is it
Created: 2025-09-05 08:03:39
How many sides does a hexagon have?
Created: 2025-09-05 08:06:35
Write the fraction of shaded squares if 6 of 10 squares are shaded?
Created: 2025-09-05 08:08:53
How many liters are in 3000 milliliters?
Created: 2025-09-05 08:11:55
What is 8 x 5?
Created: 2025-09-05 08:13:33
What is 56 ÷ 8?
Created: 2025-09-05 08:17:31
A movie starts at 3:10 PM and ends at 4:05 PM. How many minutes long is it
Created: 2025-09-05 08:20:39
How many liters are in 2000 milliliters?
Created: 2025-09-05 08:23:21
What is 6 x 7?
Created: 2025-09-05 08:26:29
What is 42 ÷ 8?
Created: 2025-09-05 08:30:45
A movie starts at 3:10 PM and ends at 4:25 PM. How many minutes long is it
Created: 2025-09-05 08:33:23
What is 20 x 6?
Created: 2025-09-05 08:38:04
What is 801 ÷ 8?
Created: 2025-09-05 08:40:17
Add 3/8 + 5/8
Created: 2025-09-05 08:43:19
Subtract 5/6 - 2/10
Created: 2025-09-05 08:46:06
An angle measures 36° more than a right angle. What is its measure
Created: 2025-09-05 08:48:23
Classify the shape with 4 equal sides and 4 right angles
Created: 2025-09-05 08:50:57
Find the factor pairs of 48?
Created: 2025-09-05 08:53:27
Round 8321 to the nearest hundred?
Created: 2025-09-05 09:00:21
A rectangle is 15 cm by 9 cm. What is the perimeter
Created: 2025-09-05 09:02:51
"Write a numerical expression for
Created: 2025-09-05 09:05:06
What is 30 x 8?
Created: 2025-09-05 09:07:38
What is 811 ÷ 8?
Created: 2025-09-05 09:09:50
Subtract 7/10 - 1/6
Created: 2025-09-05 09:12:01
Find the factor pairs of 24?
Created: 2025-09-05 09:13:47
Round 1999 to the nearest hundred?
Created: 2025-09-05 09:16:08
A rectangle is 15 cm by 7 cm. What is the perimeter
Created: 2025-09-05 09:18:13
What is 40 x 6?
Created: 2025-09-05 09:20:50
What is 821 ÷ 5?
Created: 2025-09-05 09:22:43
Add 5/6 and 3/8. Give the total
Created: 2025-09-05 09:25:13
A store sells 4 notebooks at $2.49 each and 3 pens at $1.25 each. You pay with $20.00. How much change do you receive
Created: 2025-09-05 09:27:01
"Two boxes without overlap
Created: 2025-09-05 09:29:12
A rectangle measures 2 1/2 ft by 1 3/4 ft. What is the area
Created: 2025-09-05 09:31:00
A recipe uses 1/5 cup of sugar per batch. You have 5 cups. How many batches can you make
Created: 2025-09-05 09:32:39
Compute 3.75 + 2.6
Created: 2025-09-05 09:34:43
Write the value of the digit 7 in 7.054?
Created: 2025-09-05 09:36:51
A right rectangular prism is 3 cm by 5 cm by 7 cm. What is its volume
Created: 2025-09-05 09:39:14
Add 3/4 and 2/3. Give the total
Created: 2025-09-05 09:40:43
A store sells 3 notebooks at $2.49 each and 3 pens at $1.25 each. You pay with $20.00. How much change do you receive
Created: 2025-09-05 09:43:12
A rectangle measures 4 1/2 ft by 3 3/4 ft. What is the area
Created: 2025-09-05 09:45:00
A recipe uses 1/4 cup of sugar per batch. You have 4 cups. How many batches can you make
Created: 2025-09-05 09:47:07
Compute 4.8 x 0.6
Created: 2025-09-05 09:48:55
A right rectangular prism is 3 cm by 6 cm by 8 cm. What is its volume
Created: 2025-09-05 09:51:02
Add 5/6 and 2/3. Give the total
Created: 2025-09-05 09:52:53
A store sells 5 notebooks at $2.49 each and 3 pens at $1.25 each. You pay with $20.00. How much change do you receive
Created: 2025-09-05 09:55:02
A rectangle measures 3 1/2 ft by 2 3/4 ft. What is the area
Created: 2025-09-05 10:01:29
A recipe uses 1/5 cup of sugar per batch. You have 6 cups. How many batches can you make
Created: 2025-09-05 10:05:19
Write the value of the digit 7 in 0.078?
Created: 2025-09-05 10:07:12
"The ratio of cats to dogs is 3:5. If there are 20 dogs
Created: 2025-09-05 10:10:50
Plot -2 and 3 on a number line. Which is greater?
Created: 2025-09-05 10:13:06
Solve x + 9 = 21?
Created: 2025-09-05 10:14:52
Find the area of a triangle with base 9 cm and height 7 cm?
Created: 2025-09-05 10:16:27
Find the surface area of a rectangular prism 4 cm by 4 cm by 5 cm?
Created: 2025-09-05 10:18:37
"Compute the unit rate
Created: 2025-09-05 10:21:01
"Add
Created: 2025-09-05 10:23:24
Simplify the fraction 30/24
Created: 2025-09-05 10:25:11
"Find the mean of the data
Created: 2025-09-05 10:27:26
"The ratio of cats to dogs is 3:5. If there are 32 dogs
Created: 2025-09-05 10:29:36
Plot -3 and 4 on a number line. Which is greater?
Created: 2025-09-05 10:32:11
Solve x + 8 = 23?
Created: 2025-09-05 10:33:45
Find the area of a triangle with base 8 cm and height 4 cm?
Created: 2025-09-05 10:35:16
Find the surface area of a rectangular prism 4 cm by 5 cm by 6 cm?
Created: 2025-09-05 10:37:27
Simplify the fraction 18/36
Created: 2025-09-05 10:39:26
Plot -4 and 5 on a number line. Which is greater?
Created: 2025-09-05 10:42:15
Solve x + 7 = 25?
Created: 2025-09-05 10:43:46
Find the area of a triangle with base 7 cm and height 5 cm?
Created: 2025-09-05 18:16:00
Simplify the fraction 30/42
Created: 2025-09-05 18:17:22
A store advertises 25% off a $30 shirt. What is the sale price
Created: 2025-09-05 18:18:44
"A line passes through (0
Created: 2025-09-05 18:20:33
Solve 3(x - 2) = 16?
Created: 2025-09-05 18:21:58
"Angles are supplementary
Created: 2025-09-05 18:23:44
"The scale is 1 cm : 6 m. If a room is 13 m long
Created: 2025-09-05 18:25:07
The probability of red is 3/6. What is the probability of not red
Created: 2025-09-05 18:26:39
"In a sample of 50 students
Created: 2025-09-05 22:37:54
A store advertises 25% off a $31 shirt. What is the sale price
Created: 2025-09-05 22:40:22
Solve 3(x - 2) = 18?
Created: 2025-09-05 22:43:06
"The scale is 1 cm : 7 m. If a room is 14 m long
Created: 2025-09-05 22:44:25
The probability of red is 1/4. What is the probability of not red
Created: 2025-09-05 22:45:29
A store advertises 25% off a $32 shirt. What is the sale price
Created: 2025-09-05 22:46:49
Solve 3(x - 2) = 20?
Created: 2025-09-05 22:48:06
"The scale is 1 cm : 5 m. If a room is 12 m long
Created: 2025-09-05 22:50:26
The probability of red is 2/5. What is the probability of not red
Created: 2025-09-05 22:51:30
A store advertises 25% off a $33 shirt. What is the sale price
Created: 2025-09-05 22:53:53
Solve 3(x - 2) = 22?
Created: 2025-09-05 22:56:14
Solve 2x - 5 = 13?
Created: 2025-09-05 22:58:45
"Solve the system
Created: 2025-09-05 23:00:11
A right triangle has legs 11 and 14. Find the hypotenuse
Created: 2025-09-05 23:01:29
A cylinder has radius 4 cm and height 10 cm. What is the volume
Created: 2025-09-05 23:02:52
Graph the line with slope 1/2 and y-intercept -1?
Created: 2025-09-05 23:12:29
Solve 3x - 5 = 15?
Created: 2025-09-05 23:13:42
A right triangle has legs 9 and 12. Find the hypotenuse
Created: 2025-09-05 23:16:02
A cylinder has radius 3 cm and height 11 cm. What is the volume
Created: 2025-09-05 23:17:06
Graph the line with slope 2/2 and y-intercept 1?
Created: 2025-09-05 23:26:39
Solve 4x - 5 = 17?
Created: 2025-09-05 23:30:12
A right triangle has legs 10 and 13. Find the hypotenuse
Created: 2025-09-05 23:31:29
A cylinder has radius 4 cm and height 12 cm. What is the volume
Created: 2025-09-05 23:33:01
Is y = 3x - 3 a function of x?
Created: 2025-09-05 23:39:29
Graph the line with slope 3/2 and y-intercept -2?
Created: 2025-09-05 23:43:10
Solve 2x - 5 = 14?
Created: 2025-09-05 23:44:40
A cylinder has radius 3 cm and height 10 cm. What is the volume
Created: 2025-09-05 23:46:03
"Reflect (-3
Created: 2025-09-05 23:50:44
Is y = 3x - 4 a function of x?
Created: 2025-09-05 23:51:56
Graph the line with slope 1/2 and y-intercept 0?
Created: 2025-09-05 23:55:32
Factor x^2 - 7x + 12?
Created: 2025-09-05 23:56:56
Solve (x - 4)(x + 6) = 0?
Created: 2025-09-05 23:58:15
The graph of y = 4x - 4 crosses the y-axis at what value
Created: 2025-09-05 23:59:28
Solve 2x + 3 = 8x - 9?
Created: 2025-09-06 00:01:58
Evaluate f(x) = 2x^2 - x + 3 at x = 5
Created: 2025-09-06 00:04:22
"Write the equation of a line through (1
Created: 2025-09-06 00:06:39
Simplify (2x^2)(3x^1)
Created: 2025-09-06 00:08:25
Factor x^2 - 10x + 13?
Created: 2025-09-06 00:10:01
Solve (x - 5)(x + 7) = 0?
Created: 2025-09-06 00:11:27
The graph of y = 2x - 6 crosses the y-axis at what value
Created: 2025-09-06 00:14:17
Solve 3x + 3 = 9x - 9?
Created: 2025-09-06 00:16:06
Evaluate f(x) = 2x^2 - x + 3 at x = 2
Created: 2025-09-06 00:17:33
Simplify (3x^3)(4x^2)
Created: 2025-09-06 00:19:29
Factor x^2 - 9x + 14?
Created: 2025-09-06 00:21:17
Solve (x - 3)(x + 5) = 0?
Created: 2025-09-06 00:22:53
The graph of y = 3x - 3 crosses the y-axis at what value
Created: 2025-09-06 00:24:12
Solve 4x + 3 = 10x - 9?
Created: 2025-09-06 00:25:42
Evaluate f(x) = 2x^2 - x + 3 at x = 4
Created: 2025-09-06 00:27:04
Simplify (4x^2)(3x^1)
Created: 2025-09-06 00:28:27
Factor x^2 - 8x + 15?
Created: 2025-09-06 00:30:11
The graph of y = 4x - 5 crosses the y-axis at what value
Created: 2025-09-06 00:31:41
Solve 2x + 3 = 5x - 9?
Created: 2025-09-06 00:33:26
Simplify (2x^3)(4x^2)
Created: 2025-09-06 00:40:40
"In triangle ABC
Created: 2025-09-06 00:42:49
"Find the distance between (-4
Created: 2025-09-06 00:44:19
A circle has equation (x - 2)^2 + (y + 3)^2 = 18. What is the center and radius
Created: 2025-09-06 00:46:00
"Write an equation of the line through (1
Created: 2025-09-06 00:47:34
A right triangle has angle 30° and adjacent side 9. Find the hypotenuse
Created: 2025-09-06 00:49:06
"Given parallel lines cut by a transversal
Created: 2025-09-06 00:51:28
Find the area of a circle with radius 7 cm?
Created: 2025-09-06 00:52:50
"Find the distance between (-5
Created: 2025-09-06 00:54:47
A circle has equation (x - 3)^2 + (y + 1)^2 = 20. What is the center and radius
Created: 2025-09-06 00:56:14
A right triangle has angle 30° and adjacent side 10. Find the hypotenuse
Created: 2025-09-06 00:57:34
Find the area of a circle with radius 8 cm?
Created: 2025-09-06 00:59:24
"Find the distance between (-3
Created: 2025-09-06 01:01:07
A circle has equation (x - 2)^2 + (y + 2)^2 = 17. What is the center and radius
Created: 2025-09-06 01:02:55
A right triangle has angle 30° and adjacent side 8. Find the hypotenuse
Created: 2025-09-06 01:05:19
Find the area of a circle with radius 9 cm?
Created: 2025-09-06 01:06:45
A circle has equation (x - 3)^2 + (y + 3)^2 = 19. What is the center and radius
Created: 2025-09-06 01:08:58
Solve 2^x = 32. Give x to the nearest hundredth?
Created: 2025-09-06 01:10:37
Simplify (4x^2y)(3x^3y^3)
Created: 2025-09-06 01:12:19
"Solve x/(x-5) = 2 for x
Created: 2025-09-06 01:13:33
"The function f(x) = a·b^x passes through (0
Created: 2025-09-06 01:15:39
A data set has mean 74 and standard deviation 8. What z-score corresponds to 90
Created: 2025-09-06 01:17:18
Write the recursive and explicit formulas for an arithmetic sequence with a1 = 4 and d = 5?
Created: 2025-09-06 01:19:42
Rewrite log base 2 of 16 using natural logarithms
Created: 2025-09-06 01:21:47
Solve 2^x = 56. Give x to the nearest hundredth?
Created: 2025-09-06 01:23:46
Simplify (3x^2y)(2x^3y^2)
Created: 2025-09-06 01:25:49
"Solve x/(x-3) = 2 for x
Created: 2025-09-06 01:27:22
A data set has mean 75 and standard deviation 9. What z-score corresponds to 91
Created: 2025-09-06 01:29:13
Write the recursive and explicit formulas for an arithmetic sequence with a1 = 2 and d = 3?
Created: 2025-09-06 01:31:49
Rewrite log base 3 of 20 using natural logarithms
Created: 2025-09-06 01:33:45
Solve 2^x = 48. Give x to the nearest hundredth?
Created: 2025-09-06 01:35:22
"Solve x/(x-4) = 2 for x
Created: 2025-09-06 01:37:00
A data set has mean 70 and standard deviation 8. What z-score corresponds to 86
Created: 2025-09-06 01:39:19
Write the recursive and explicit formulas for an arithmetic sequence with a1 = 3 and d = 4?
Created: 2025-09-06 01:41:56
Solve log_3(x) + log_3(x-2) = 2 for x > 2?
Created: 2025-09-06 01:44:08
"For f(x) = (2x)/(x-2)
Created: 2025-09-06 01:47:01
"The sequence is a1 = 2
Created: 2025-09-06 01:50:07
A normal distribution has mean 103 and sigma = 15. What percentile is x = 128
Created: 2025-09-06 01:51:52
Solve for q in 1/p + 1/q = 1/6?
Created: 2025-09-06 01:56:05
Find the inverse of f(x) = (x - 4)/(4x + 1)?
Created: 2025-09-06 01:58:47
Use the binomial theorem to expand (x + 2)^3
Created: 2025-09-06 02:01:10
Solve log_3(x) + log_3(x-3) = 2 for x > 3?
Created: 2025-09-06 02:03:23
"For f(x) = (2x)/(x-1)
Created: 2025-09-06 02:05:01
A normal distribution has mean 100 and sigma = 16. What percentile is x = 125
Created: 2025-09-06 02:07:25
Solve for q in 1/p + 1/q = 1/7?
Created: 2025-09-06 02:09:18
Find the inverse of f(x) = (x - 2)/(3x + 1)?
Created: 2025-09-06 02:11:33
Use the binomial theorem to expand (x + 3)^3
Created: 2025-09-06 02:13:32
A normal distribution has mean 102 and sigma = 17. What percentile is x = 127
Created: 2025-09-06 02:15:12
Find the inverse of f(x) = (x - 3)/(4x + 1)?
Created: 2025-09-06 02:17:18
什么是滴定
Created: 2025-09-08 08:03:39
Teach me how to fix a motorcycle engine
Created: 2025-09-08 08:33:23
Explain photosynthesis
Created: 2025-09-08 09:10:28
educacion
Created: 2025-09-08 09:22:00
Hi
Created: 2025-09-08 09:36:39
Hi
Created: 2025-09-08 09:36:30
解准好劃是如之
Created: 2025-09-08 10:19:23
在离散数学中,什么是关系
Created: 2025-09-09 05:34:28
如何使用矩阵表示离散数学中的关系
Created: 2025-09-09 08:00:17
印度食物有什么特点
Created: 2025-09-09 08:10:49
中国食物有什么特点
Created: 2025-09-09 08:21:11
为什么说水是声明之源
Created: 2025-09-09 10:45:01
讲解人体结构
Created: 2025-09-09 10:51:56
什么是web3
Created: 2025-09-09 19:38:23
什么是加密货币
Created: 2025-09-09 20:04:49
csc,sec,cot 在三角函数中分别是什么函数
Created: 2025-09-11 03:07:37
同位语
Created: 2025-09-12 06:13:20
二维码的原理
Created: 2025-09-12 15:25:59
生活中肉蛋奶
Created: 2025-09-18 07:11:58
PCR技术
Created: 2025-09-21 02:49:00
如何管理时间
Created: 2025-10-02 08:04:55
svg 如何现实数学公式
Created: 2025-10-07 08:00:26
在 html中,什么是 canvas
Created: 2025-10-07 08:19:47
什么是空间向量
Created: 2025-10-07 12:34:21
什么是向量的点积
Created: 2025-10-07 12:37:56
使用foreignObject+ html 演示太阳系的行星运动
Created: 2025-10-07 12:41:11
什么是矩阵的相乘
Created: 2025-10-07 12:50:55
异步和事件循环如何提高服务器的并发
Created: 2025-10-07 12:52:11
await会阻塞线程吗？
Created: 2025-10-07 13:23:52
svg如何插入图片
Created: 2025-10-07 19:02:44
四个人年龄之和是77岁,年龄最小的是10岁,最大的与最小的年龄之和比另外两个人的年龄之和大7岁,年龄最大的人多少岁?
Created: 2025-10-07 19:26:43
数据在网络中是如何传输的
Created: 2025-10-07 19:36:58
how to recognize all three 2D conic curves (parabola, hyperbola, ellipse) so that you can identify
planar cross-sections of quadric surfaces
Created: 2025-10-07 19:48:04
how to to graph a parametric curve in 2D.
Created: 2025-10-07 19:56:13
how to parametrize a Cartesian equation.
Created: 2025-10-07 20:03:06
Find the slope of the tangent line, critical values, periods of increasing/decreasing for a curve
defined by parametric equations
Created: 2025-10-07 20:09:43
如何计算r=4sin theta的面积
Created: 2025-10-07 22:06:12
如何计算 r=2sin(2theta)的面积
Created: 2025-10-07 22:31:33
Classify the quadric surface.
4x2 − y2 − z2 = 1
Created: 2025-10-07 22:45:58
Classify the quadric surface.
z2 = x2 + y2/9
Created: 2025-10-07 22:57:19
人工智能知识体系编程与工具之版本控制Git
Created: 2025-10-07 23:57:23
人工智能知识体系编程与工具之版本控制Git
Created: 2025-10-08 00:05:46
万以内数的认识
Created: 2025-10-08 00:27:14
线面角：(1)向量法公式，(2)几何法公式
Created: 2025-10-08 02:35:18
已知道两点,如何直线的方程
Created: 2025-10-08 20:16:46
如何计算点到直线的举例
Created: 2025-10-08 20:50:29
如何计算向量的点积
Created: 2025-10-09 06:08:37
3.4：实证验证 —— 系列位置效应与记忆系统的独立性 核心任务：通过 “自由回忆实验”，让学生在规定时间内记忆 20 个无关联单词，随后自由写出记住的单词，统计每个单词的回忆正确率。 分析：绘制 “系列位置曲线”，识别 “首因效应”（前几个单词正确率高，因进入长时记忆）和 “近因效应”（最后几个单词正确率高，因仍在短时记忆），验证记忆系统的分段存储特性。
Created: 2025-10-09 06:47:10
如何计算单位向量
Created: 2025-10-09 06:47:28
什么是向量的cross product
Created: 2025-10-09 07:03:09
什么是向量的dot product
Created: 2025-10-09 07:25:55
如何计算切线和求导
Created: 2025-10-09 07:32:27
讲述一下人工智能发展历史
Created: 2025-10-09 07:42:15
介绍和向量相关的公式
Created: 2025-10-09 08:15:42
和向量相关的公式都有那些
Created: 2025-10-09 08:23:25
和向量相关的公式有那些
Created: 2025-10-09 09:47:42
演示牛顿第二定律
Created: 2025-10-09 10:00:16
和导数相关的公式都有有那些
Created: 2025-10-09 10:06:58
和平面向量相关的公式有那些
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在平面向量中,已知两点,如何求角度
Created: 2025-10-09 10:46:35
讲解什么时三角形,标出三角形各个角的角度,不要是用svg 的 path 路径画角的弧度,使用 javascrpt计算然后在给角度添加标签
Created: 2025-10-10 00:59:19
讲解什么时三角形,标出三角形各个角的角度,不要是用svg 的 path 路径画角的弧度,使用 javascrpt计算然后在图形上绘制, 不要是用 text的绝对定位给我图形添加标签 而是给 circle一个 id根据 circle 的位置是用 javascript计算标签的位置
Created: 2025-10-10 01:06:14
讲解什么时三角形,标出三角形各个角的角度,不要是用svg 的 path 路径画角的弧度,使用 javascrpt计算然后在图形上绘制, 不要是用 text的绝对定位给我图形添加标签 而是根据 circle 的位置是用 javascript计算标签的位置. 三角形和多边形 的 点 的坐标值 也不要写死,而是是用 javascript 自行计算
Created: 2025-10-10 01:22:54
讲解什么时三角形,标出三角形各个角的角度,不要是用svg 的 path 路径画角的弧度,使用 javascrpt计算然后在图形上绘制, 不要是用 text的绝对定位给我图形添加标签 而是根据 circle 的位置是用 javascript计算标签的位置. 三角形的 点 的坐标值 根据角度值计算
Created: 2025-10-10 01:28:15
讲解什么是三角形,各个角的角度
不要用 svg 的 path 路径画角的弧度,使用计算然后在图形上绘制,
不要用 text的绝对定位给我图形添加标签 而是根据 点的位置 的位置算标签的位置.
三角形等多边形 的 点 的坐标值也根据角度值计算.
Created: 2025-10-10 01:34:08
讲解什么时三角形,标出三角形各个角的角度,
不要是用svg 的 path 路径画角的弧度,使用 javascrpt计算然后在图形上绘制.
不要是用 text的绝对定位给我图形添加标签 而是根据 circle 的位置是用 javascript计算标签的位置.
三角形的 点 的坐标值 根据角度值计算.
四角形的 点 的坐标值 根据角度值计算.
多边形的 点 的坐标值 根据角度值计算.
Created: 2025-10-10 01:39:07
讲解什么时三角形,标出三角形各个角的角度,
不要是用 text的绝对定位给我图形添加标签 而是是用 javascript 根据 circle 的位置计算
不要是用svg 的 path 路径画角的弧度,根据circle计算然后绘制.
点 的坐标值 根据角度值计算.
Created: 2025-10-10 01:42:53
讲解什么时三角形,标出三角形各个角的角度,
不要是用 text的绝对定位给我图形添加标签 而是是用 javascript 根据 circle 的位置计算
不要是用svg 的 path 路径画角的弧度,根据边计算然后绘制.
点 的坐标值 根据角度值计算.
Created: 2025-10-10 01:44:47
讲解什么时三角形,标出三角形各个角的角度,
不要是用 text的绝对定位给我图形添加标签 而是是用 javascript 根据 circle 的位置计算
不要是用svg 的 path 路径 标记 角的弧度,而是根据 circle计算然后绘制.
点 的坐标值 根据角度值计算.
Created: 2025-10-10 01:47:58
讲解什么时三角形,标出三角形各个角的角度.
注意,下面是注意事项,不是主题的一部分
禁止用 text的绝对定位给我图形添加标签 而是是用 javascript 根据 circle 的计算tex位置
禁止用 svg 的 path 路径 标记 角的弧度,而是根据 circle计算然后绘制.
先确定一个或者两个点,其他点 的坐标值 根据角度值计算.
Created: 2025-10-10 01:51:18
什么是向量值函数
Created: 2025-10-10 02:13:29
什么是路易斯结构
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量子隧穿
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天文学
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勾股定理
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什么是三角形
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为什么冰可乐更好喝
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Topic 11: Recurrence Relations
Created: 2025-10-13 22:22:57
Topic 12: Solving Recurrence Relations & Applications to Big-O
Created: 2025-10-13 23:26:04
Section 12.2: Differentiation and Integration of Vector-Valued Functions
Created: 2025-10-15 01:14:32
我要做刚体定轴转动的角动量守恒的动画 模型创建新建一个 “圆柱 + 伸展臂” 的刚体模型：圆柱代表转轴，两侧添加可伸缩的长方体 “臂”（模拟转动惯量变化的结构）。给模型添加 “刚体动力学” 属性，设置初始转动惯量关联 “臂的长度”（臂越长，转动惯量 I 越大）。物理参数与关键帧设置初始状态：设置臂完全伸展，转动惯量 \(I_1 = 2 \, \text{kg·m}^2\)，初始角速度 \(\omega_1 = 5 \, \text{rad/s}\)，记录为第 1 个关键帧（时间 \(t = 0\)）。变化过程：在 \(t = 2 \, \text{s}\) 处插入关键帧，将臂收缩至一半长度，此时转动惯量 \(I_2 = 1 \, \text{kg·m}^2\)。根据角动量守恒 \(L = I_1\omega_1 = I_2\omega_2\)，计算得 \(\omega_2 = 10 \, \text{rad/s}\)，设置此时角速度为 \(10 \, \text{rad/s}\)。后续运动：在 \(t = 4 \, \text{s}\) 处，再将臂完全收缩，转动惯量 \(I_3 = 0.5 \, \text{kg·m}^2\)，计算得 \(\omega_3 = 20 \, \text{rad/s}\)，设置角速度并记录关键帧，让刚体持续以 \(\omega_3\) 转动至动画结束（\(t = 6 \, \text{s}\)）。交互与可视化增强用 Blender 的 “驱动” 功能，将 “臂的长度滑块” 与 “转动惯量属性” 绑定，实现交互调节（模拟前文 “AI 交互参数调节”）。添加 “文本对象”，实时显示当前转动惯量 I、角速度 \(\omega\)、角动量 L 的数值，并制作 “\(I - t\)”“\(\omega - t\)” 的动态曲线（通过 “动画曲线编辑器” 实现）。三、动画效果演示（文字描述）动画开始时，刚体（带伸展臂）以较慢的速度 \(\omega_1 = 5 \, \text{rad/s}\) 转动；随着臂逐渐收缩，转动惯量减小，角速度逐渐加快；当臂完全收缩后，刚体以更快的速度 \(\omega_3 = 20 \, \text{rad/s}\) 稳定转动。过程中，屏幕旁的文本实时刷新 I、\(\omega\)、L 的数值，动态曲线也同步变化，直观体现 “合外力矩为零时，角动量守恒，I 与 \(\omega\) 成反比” 的物理规律。
Created: 2025-10-15 16:43:11
系统会自动匹配物理类模板，在 “推荐模板” 中选择 “角动量守恒 - 刚体转动” 模板（若未显示，可在左侧 “物理→力学→转动运动” 分类中手动查找）；点击模板预览图，进入 “动画编辑界面”，此时界面已默认加载 “转轴 + 伸缩臂转轮” 的基础模型，以及初始参数（如初始\(I_1=2\ \text{kg·m}^2\)，\(\omega_1=5\ \text{rad/s}\)，\(L=10\ \text{kg·m}^2/\text{s}\)）。3. 调整刚体模型与物理参数模型调整：在左侧 “模型编辑” 栏，点击 “伸缩臂” 组件，拖动 “长度调节滑块”，设置 “伸展状态长度”（如 10cm，对应\(I_1=2\ \text{kg·m}^2\)）和 “收缩状态长度”（如 5cm，对应\(I_2=1\ \text{kg·m}^2\)），模型会实时同步伸缩效果；参数绑定：在 “物理参数” 栏，勾选 “自动关联角动量公式”，系统会根据\(L=I\omega\)自动计算：当I从 2 变为 1 时，\(\omega\)从 5 变为 10（确保L始终为 10），无需手动输入数值。4. 添加动态交互与数据展示交互设置：在右侧 “交互控制” 栏，点击 “添加触发条件”，选择 “时间触发”，设置 “0-2 秒：伸缩臂伸展→转动（\(I=2\)，\(\omega=5\)）”“2-4 秒：伸缩臂收缩→转动加速（\(I=1\)，\(\omega=10\)）”“4 秒后：保持收缩状态匀速转动”，动画会按时间线自动切换状态；数据可视化：在 “数据展示” 栏，勾选 “实时数值显示” 和 “参数变化曲线”，选择显示I、\(\omega\)、L三个物理量，设置数值字体大小（建议 16 号，适配观看），曲线颜色可区分（如I用蓝色，\(\omega\)用红色，L用绿色）。5. 优化动画细节与场景场景添加：在 “背景设置” 中，选择 “实验室场景”（含坐标轴、参考刻度），帮助观众判断转动速度变化；语音与字幕：在 “旁白字幕” 栏，点击 “自动生成解说”，系统会根据物理原理生成配音（如 “当伸缩臂收缩，转动惯量减小，角速度增大，角动量保持不变”），可调整语速与音量，字幕会同步显示在动画底部。6. 预览与导出动画视频预览测试：点击顶部 “预览” 按钮，播放动画，观察 3 个关键效果：伸缩臂收缩时，转轮转动速度是否加快；数据栏中L是否始终为 10；曲线是否清晰呈现I下降、\(\omega\)上升的反比关系，若有偏差，返回步骤 3 重新调整参数；导出设置：预览无误后，点击 “导出”，选择 “视频格式”（如 MP4）和 “清晰度”（建议 1080P），等待 1-2 分钟，完成后点击 “下载”，即可获取可直接使用的动画视频。
Created: 2025-10-15 16:57:18
### （1）AI交互内容和包含的物理原理定理（以“跳水运动员抱膝翻转”为例）
- **AI交互内容**：
- **可调节参数**：
- 运动员初始转动惯量 \( I_1 \)（范围 \( 10 - 20 \, \text{kg·m}^2 \)，通过“身体伸展程度”滑块调节，伸展时 \( I \) 大，蜷缩时 \( I \) 小）；
- 初始角速度 \( \omega_1 \)（范围 \( 1 - 5 \, \text{rad/s} \)，通过“起跳旋转速度”滑块调节）。
- **交互操作**：
- 点击“开始”按钮，动画展示运动员从“伸展（\( I_1 \)）、角速度 \( \omega_1 \)”状态，逐渐蜷缩身体（转动惯量变为 \( I_2 \)），观察角速度增大的过程；
- 点击“暂停”可定格任意时刻，查看当前转动惯量 \( I \)、角速度 \( \omega \)、角动量 \( L \) 的数值；
- 点击“重置”恢复初始参数（默认 \( I_1 = 15 \, \text{kg·m}^2 \)，\( \omega_1 = 2 \, \text{rad/s} \)）。
- **数据展示**：
实时显示：
- 转动惯量 \( I \)（随身体蜷缩/伸展动态变化，如蜷缩时 \( I_2 = 5 \, \text{kg·m}^2 \)）；
- 角速度 \( \omega \)（根据 \( L = I_1\omega_1 = I_2\omega_2 \) 实时计算，如 \( \omega_2 = \frac{I_1\omega_1}{I_2} = 6 \, \text{rad/s} \)）；
- 角动量 \( L \)（始终为 \( L = 15 \times 2 = 30 \, \text{kg·m}^2/\text{s} \)，验证守恒）。
- **包含的物理原理定理**：
刚体定轴转动的角动量守恒定律：跳水运动员在空中时，重力和水的浮力（未入水时）对其质心的力矩近似为零，系统角动量 \( L = I\omega \) 守恒。当运动员蜷缩身体（减小转动惯量 \( I \)），角速度 \( \omega \) 会增大；伸展身体（增大转动惯量 \( I \)），角速度 \( \omega \) 会减小，以此完成快速翻转或平稳入水。
### （2）网页版成果物（简要描述）
- **界面布局**：
- 左侧：参数调节区，包含“身体伸展程度（对应 \( I \)）”“起跳旋转速度（对应 \( \omega_1 \)）”的滑块，以及“开始/暂停/重置”按钮；
- 中间：动画展示区，用矢量图形绘制跳水运动员（可动态蜷缩/伸展身体），实时演示空中翻转过程；
- 右侧：数据展示区，包含“转动惯量 \( I \)”“角速度 \( \omega \)”“角动量 \( L \)”的实时数值，以及 \( I - t \)、\( \omega - t \) 的动态变化曲线（曲线颜色区分：\( I \) 为蓝色，\( \omega \) 为红色，\( L \) 为绿色水平直线）。
- **功能特点**：
- **参数可调**：拖动滑块改变 \( I_1 \) 或 \( \omega_1 \)，动画实时响应，角速度和转动惯量同步变化，直观体现 \( I \) 与 \( \omega \) 的反比关系；
- **可视化强**：运动员蜷缩时转动加快、伸展时转动减慢的动画效果，结合数据曲线，清晰展示角动量守恒的动态过程；
- **功能性强**：支持“开始/暂停/重置”交互，且通过数值和曲线对比，能深入理解“合外力矩为零，角动量守恒”的物理内涵。
Created: 2025-10-15 17:19:21
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Created: 2025-10-22 19:54:38
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