跑步打卡
2025年4月 周一 周二 周三 周四 周五 周六 周日 14 15 16 17 18 19 205.6km 21 22 235.6km 245.6km 25 26 27 28 29 30 2025年5月 周一 周二 周三 周四 ...
向量代数与空间解析几何习题总结
type one：给一条直线求绕轴旋转的曲面方程 直线 L:x−12=y−2−1=z1L: \frac{x-1}{2} = \frac{y-2}{-1} = \frac{z}{1}L:2x−1=−1y−2=1z 绕 zzz 轴旋转而成的曲面为______. 这一道题有点迷啊 以下讨论是在M和M0M_{0}M0在z坐标相同的那一个圆中进行的 设M：（x，y，z）是曲面上的任意一点，M0：(x0,y0,z)M_{0}：(x_{0},y_{0},z)M0：(x0,y0,z)是直线上的一点 原点设为R:(0,0,z) 可以得到这个关系：∣MR∣=∣MM0∣|MR|=|MM_{0}|∣MR∣=∣MM0∣，然后把x0,y0x_{0},y_{0}x0,y0用z来代替就得出结果了 不过还是好奇怪，就是理不清思路 搁置吧 type two：求点到直线的距离（这个重要） 点 M(2,1,1)M(2, 1, 1)M(2,1,1) 到直线 L:x−11=y−10=z−1L: \frac{x-1}{1} = \frac{y-1}{0} =...
words-eleventh-day
单词释义 sentiment - n. paraphrase：a feeling or opinion synonym：feeling, thought, view example：Although the team lost the game, there was a positive sentiment among the players because they had played their best, which made the coach proud. reign - n./v. paraphrase：(n.) the period when a king or queen rules a country; (v.) to rule as king or queen synonym：rule, govern, period example：During her reign, the queen introduced many reforms, which improved the lives of her people, and she was...
10 Emerging Technologies That Will Shape the Next Decade
video link [Segment 1: Introduction] We talk a lot about AI, crypto, and space exploration when we discuss the future, but there’s this whole universe of emerging technologies that don’t get enough attention. Technologies that could fundamentally reshape our world in the next decade. And that’s exactly what we are going to talk about today. [Segment 2: Video engagement] We are going to go through some of the emerging the top emerging technologies over the next decade that will change well...
word-tenth-day
单词释义 reverse - v./n./adj. paraphrase：to go backward or change to the opposite synonym：undo, invert example：If you accidentally delete a file, you can reverse the action by pressing Ctrl+Z, which is a handy feature unless you’ve already closed the program. refute - v. paraphrase：to prove something wrong synonym：deny, disprove example：Although the scientist presented strong evidence, her critics tried to refute her claims by pointing out minor flaws in the data. household...
words-ninth-day
单词释义 mature - adj./v. paraphrase：fully grown or developed synonym：grown, ripe, adult example：Although the fruit looks ripe, it needs more time to mature before we can eat it. imminent - adj. paraphrase：about to happen very soon synonym：approaching, nearing example：The storm clouds suggest rain is imminent, so we should hurry home unless we want to get wet. convention - n. paraphrase：a formal meeting or accepted way of doing things synonym：conference,...
words-eighth-day
单词释义 governor - n. paraphrase：a person who controls a region or organization synonym：leader, ruler example：Although the governor proposed new policies, many citizens disagreed because they felt the changes were unfair. acute - adj. paraphrase：very serious or severe synonym：intense, sharp example：The doctor said the pain was acute, so she prescribed medicine which would help reduce it quickly. organism - n. paraphrase：a living thing, like a plant or...
确定化与最小化
确定化 用画表法 第一步：第一列写出所有的状态，第一行写出所有的弧名 状态应该不是所有节点的排列组合，要不先把所有单个节点的状态写出来，然后单个节点推出来新的状态之后再把这个新状态写到第一列 第二步：给左边第一列的所有状态编号，0、1、2、……，然后把表中的所有状态用编号代替 第三步：根据这个编号得出的新表画出确定化的图 什么是终态终态：原图上的终态，和包含所有节点的状态 举个例子 最小化 记住一句话，分组后的元素，经过a弧到达的状态在同一组中，经过b弧到达的状态也在同一组中（这两个组不一定相同） 根据上一个得出的确定化图写 第一步：分组，把非终态分成一组，把终态分成一组 对两个组分别用相同的方法进行处理，所以光以非终态组为例说明 第二步：写出每一个元素通过a弧的状态 第三步：看是否在同一组中，是的话直接看通过b弧的状态，不是的话，把不同的状态按相同的组进行分类 第四步：看分了之后的组通过b弧的状态，这些状态在同一个组中的话，那么这些状态就可以合并
words-seventh-day
释义列表 nevertheless - adv. paraphrase：in spite of that synonym：however, still example：The weather app predicted rain; nevertheless, we went hiking because we trusted the sunny patches breaking through the clouds. humble - adj. paraphrase：not proud, simple synonym：modest, plain example：Although he won the award, his humble speech focused on thanking his team rather than his own achievements. scope - n. paraphrase：the range of something synonym：extent, range example：The project’s...
理解积分
理解三重积分的方式 一重积分可以用面积理解，二重积分可以用体积理解，三重积分显然无法用这种方法理解，我如何理解三重积分 物理量的总和：当被积函数表示密度（如质量密度、电荷密度）时，三重积分的结果是该物理量在三维区域内的总量。例如，物体的总质量可通过积分密度函数得到。 概率与统计：若被积函数是概率密度函数，三重积分可计算三维区域内事件发生的概率。 几何测度：当被积函数恒为1时，三重积分的结果即为区域的体积，此时与几何直观一致。 数学抽象：作为多维空间中的累积操作，三重积分可视为在三个独立方向上的加权求和，无需依赖四维几何直观，而是通过逐次积分或坐标变换进行计算。 物理定律应用：如高斯定理中，三重积分用于计算场源（如电荷总量），与曲面积分结合揭示物理规律。 使用质量密度理解三重积分 假设有一个三维物体，其质量密度随位置变化，我们可以用三重积分求出它的总质量。这个例子将帮助你建立对三重积分的直观理解。 例子：计算一个长方体的总质量 问题设定： 假设有一个长方体物体，占据空间区域： xxx 方向范围：0≤x≤20 \leq x \leq...