TongZhuo's Blog

video link So today, what I want to do is talk to you about the most important conversations you have each day: the conversations you have with yourselves. My name is Ethan Cross. I’m the director of the Emotion and Self-Control Lab at the University of Michigan. For the past 25 years, I’ve been studying how people can manage their emotions. And one of the things that I’ve learned during that time - see, I’m managing my emotions right now - is that a key to managing one’s emotions...

数据结构 ![[Pasted image 20250802155839.png]] ![[Pasted image 20250802155945.png]]![[Pasted image 20250802160004.png]] ![[Pasted image 20250802160104.png]]![[Pasted image 20250802160128.png]] ![[Pasted image 20250802160145.png]]![[Pasted image 20250802160155.png]] ![[Pasted image 20250802160211.png]]![[Pasted image 20250802160220.png]] 计算机组成原理和操作系统 ![[Pasted image 20250802163135.png]] double占8个字节，AH（十六进制）是1010B（二进制），4个芯片用两位编号![[…/…/img/in-post/Pasted image 20250802164716.png]]

单词释义 statistics - n. paraphrase: the study of numbers and data to understand trends synonym: data, figures example: Although I find math challenging, I enjoy statistics because it helps me analyze where my spending habits need adjustment, such as when I track monthly expenses. foam - n. paraphrase: a light, bubbly substance formed on liquids synonym: bubbles, froth example: If you pour soda too quickly, it creates foam which spills over, whereas water doesn’t do this unless...

type one：拆分所给的向量组 设向量组α1,α2,α3\boldsymbol{\alpha}_1,\boldsymbol{\alpha}_2,\boldsymbol{\alpha}_3α1​,α2​,α3​线性无关，且α1+aα2+4α3\boldsymbol{\alpha}_1 + a\boldsymbol{\alpha}_2 + 4\boldsymbol{\alpha}_3α1​+aα2​+4α3​, 2α1+α2−α32\boldsymbol{\alpha}_1 + \boldsymbol{\alpha}_2 - \boldsymbol{\alpha}_32α1​+α2​−α3​, α2+α3\boldsymbol{\alpha}_2 + \boldsymbol{\alpha}_3α2​+α3​线性相关，则a=a=a=____。 (α1+aα2+4α3,2α1+α2−α3,α2+α3)=(α1,α2,α3)(120a114−11)(\boldsymbol{\alpha}_1 + a\boldsymbol{\alpha}_2 +...

行列式 type one：余子式与代数余子式 设A为三阶矩阵，A的第一行元素为1，2，3，|A|的第二行元素的代数余子式分别为a+1，a-2，a-1，则a= ____。 这个利用行列式的展开来解，某一行的元素乘以对应的代数余子式相加就是行列式的值 这里给出了第二行的代数余子式，把第二行的元素填充为第一行的元素，那么这个行列式有两个相同比例的行所以结果就是0 得出式子由 (a + 1) + 2(a - 2) + 3(a - 1) = 0 得 a = 1。 注：余子式是不带符号去掉这个元素所在行列剩下元素组成的行列式；代数余子式是带上符号的余子式，这个符号是(−1)行数加列数(-1)^{行数加列数}(−1)行数加列数 type...

type one：求级数的和函数 一定一定要牢记那五个麦克劳林公式 一定一定要记得先求收敛半径和收敛域 通过裂项求 （这个比较简单，不总结了 例题：∑n=1∞1(2n−1)(2n+1)=\sum_{n=1}^{\infty} \frac{1}{(2n-1)(2n+1)} =∑n=1∞​(2n−1)(2n+1)1​= 通过求导 ∑n=0∞n2xn 的和函数为 S(x)=____.\sum_{n=0}^{\infty} n^2 x^n \text{ 的和函数为} \, S(x) = \_\_\_\_.∑n=0∞​n2xn 的和函数为S(x)=____. 答案 S(x)=∑n=0∞n2xn=∑n=1∞n2xn=∑n=1∞[n(n−1)+n]xn=∑n=2∞n(n−1)xn+∑n=1∞nxn=x2∑n=2∞n(n−1)xn−2+x∑n=1∞nxn−1=x2(∑n=2∞xn)′′+x(∑n=1∞xn)′=x2(x21−x)′′+x(x1−x)′=x2+x(1−x)3.\begin{aligned} S(x) &= \sum_{n=0}^{\infty} n^{2} x^{n}...

video [Segment 1: Opening Challenge - Looking for Non-Manufactured Items] As we get started, I wanted to first ask everyone to set aside any thoughts on current events for the moment, and let’s take five seconds to look around this big room we’re all in right now, to try to find even one thing that was not manufactured. Other humans don’t count. Ready? Go. Make eye contact when you’re done. One thing that’s not manufactured. Not actually that easy, is it? [Segment 2: Manufacturing’s Global...

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项目地址 STM32F103C8T6引脚分配总览 引脚（STM32） 连接说明 红外循迹TCRT5000 5路 IR_L2 PA8 最左 IR_L1 PA9 左 IR_M PA10 中 IR_R1 PA11 右 IR_R2 PA12 最右 电机驱动（L298N等） 左电机IN1 PA2 方向 左电机IN2 PA3 方向 右电机IN1 PA4 方向 右电机IN2 PA5 方向 左电机PWM PA6 使能 右电机PWM PA7 使能 MPU6500 项目结构 123456789101112131415161718192021222324--- 自动行驶小车 --- USER --- inc car_control.h delay.h encoder.h I2C.h led.h motor.h mpu6500.h sensor.h system_config.h ---...

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