Simon's Insight

新的Blog在这里。

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Should Elders Make Decisions for Teens?

The life in the contemporary world is full of decisions, such as whether to making an investment or purchasing a car. When we were very small, parents or the other elders made decisions for us without saying. However, as we gradually grew up, we begin to have our own thought, and wanted to make our own choices. Our parents, however, still regard us as mere kids. Should they make decisions for us? In my opinion, parents should let children decide themselves.

Firstly, it is mostly beneficial to let teenagers decide themselves. In the period of teenager, one is in the preparation of the adulthood. Along with the rapid physical growth, the personal awareness of teenager is booming. The intention of fulfilling his/her will is stronger than ever before. Differ from their childhood; teenagers are smart enough to think strategically, they are capable enough as well to receive the negative consequences that decisions may issue in. Moreover, they can learn from their mistakes. Since the decisions which available for teenagers are basically not vital, most of the consequences wouldn't be very hard to overcome. Thus, the age of 15-18 is a good time for one to learn how to make decisions.

In addition, do-all parents are not good parents. Since the personal awareness of teenager is growing stronger, parents who do-all are going against the current. The teens may stick in doing what they want despite the confrontation and pressure from their parents. Conflicts will definitely break out, and the relationship between parents and children will be dangerously deteriorated. If, sadly, parents never let child to have any chance, he/she might miss the valuable time to learn the art of decision before coming to adulthoods, in which the consequences of a failed decision can be really serious.

Lastly, Teenagers still need help, even though they should be allowed to make decision on their own. The advice from parents is quite necessary. Anyway, as elders, parents usually possess more knowledge and life experience than child. Parents' words are always effective to their children. Child is child, after all.

All in all, parents are supposed to teach children how to decide things, rather than make decisions for them. As the famous movie - Dead Poet Society tells us, teenagers have their own values and goals. Parents should play roles of instructors and guides, rather than jail guards.

本来应该还要加入一个论点，说青少年善于接受新事物之类的...但是考虑到是考场作文，不现实... 

说起来距离我一生中第一次托福考试只有一个月了，我才慢悠悠地开始准备。一开始做了下模拟题。在下午炎热的空气中，看上去永远做不完的题目让我越做越烦...好吧，为了将来还是要好好做。

以后每天写一篇托福考场作文。一是要练习各种题材和体裁，二是要逐渐提高速度。在短短的30分钟内，码出一篇像样的文章对谁都不是简单的事情。在这里写的好处就是可以有群众监督，避免自己偷懒。

热烈欢迎一切批评.....鼓励也适当给一点，毕竟还有一个月了要增强信心。

Should Students Do Homework?

To students, the best homework is no homework. This statement has always been true since the first school in the history. Teachers are never weary of assigning homework to students. Does the homework really matter? My opinion is: it really does. I think doing homework is necessary for all students, since it helps learning the subject better, develops problem solving skill, and forms good habits of punctuality and responsibility.

Firstly, homework can help student learn the subject better. It is wildly acknowledged that students who do homework regularly are likely to receive better scores in the exam than the students who do not do homework. Homework can help student in many ways. For example, it can refresh the content from the classroom. As studies in psychology shows, in the pattern of oblivion, people forget things most quickly shortly after they first learnt them. Thus, reviewing the lesson after a day in school helps students keep them fresh in mind.

Moreover, homework can improve students' problem solving skill. In mathematics and scientific courses, the ability to solve problems is very important. Since few people is talented enough to solve any problem given, a fair amount practice is indeed required for most students. Teachers can teach students the concepts and some typical ways to solve certain kinds of problems. Nevertheless, the understanding of the concept and the innovative thinking are left for students to learn by themselves. By working on a variety of problems, students can not only be able to get the hang of the concepts and manipulate the typical ways of solving, but also be able to come up with their own idea. Therefore, homework can improve students' problem solving skill.

In addition, regular homework can help students form good habit. Students are obligate to finish their homework in time and are responsible for its quality. Thus, they can form habits of punctuality and responsibility by doing homework regularly. Good habit does not only affect the exam scores, but also has a huge impact on students' future.

In a word, homework can help students learn the subjects better, improve their problem solving skill, and help them form a good habit of finishing work in time. Therefore, doing homework is significant and compulsory for all students. 

开始持续上课。老师说因为我们这课节奏很快的，基本上两天上一个单元，所以今天下午就把矩阵考掉吧～

“哇...” 同学们杀猪般地叫了起来...

矩阵这个东西真神奇哎，可以大规模地处理很多很多数据，而且只要一步就可以了。嗯，传说是俺们中国老祖宗发明的喔！用途很多很广，计算很机械很无脑..... 这样直接导致我们都使用Graphing Calculator了...这么机械的步骤就交给程序吧～不过数学题目就比较讨厌的，都会在矩阵里加x和y什么的东西...

不过那个coding倒是挺好玩的。用特殊的矩阵给信件加密... 

吉他吉他。因为以前学过长笛，所以学起来不像第一次接触乐器那么不舒服。学得顺手的。就是呢，现在感觉左手中指和无名指在第三和第二根弦上换的时候，就是低音6和中音2那个，感觉有点笨的。据说无名指其实是和中指用一根筋的，怎么搞的啦～春风来解释下～～

最后TJ生日快乐，你小子终于也18岁了哇咔咔...18岁的不孤单不孤单...嘻嘻

越来越热，越来越热。即使是北纬42度，太阳感觉还是好高。而且日照时间长，晚上9点半天才黑，中午的时候真是那个炙烤的热啊！ 晚上热死了，睡都睡不着，电风扇开起来把我贴在墙上的单词纸吹得呼呼直响。早上起来一看，又是“梦里花落知多少了”。

哇，这么热的天，又要开始上课了，要上到八月一号！哇...不过其实我还是挺期待上课的，因为，整个教学楼都是空调哇！好冷啊，嘻嘻，要穿长袖！我觉得只要北美的所有的空调夏天开高一度，那个CO2的排放就要减少好多。

人生啊，起先以为这个Data Management就是画画图，统计表格啊什么的。结果第一节课居然讲Matrices，矩阵。好吧，那就学吧...反正也就是学数学么～不要紧。话说那个老师的计算能力让我颇为吃惊。没见过白人心算也可以算得这么快...

今天回来看，家里冰箱里的饮料也喝完了... 完了...晚上要死的了。

最近开始玩吉他～嘿嘿，自己学。

今天下午和两个同学和他们两家去采樱桃去了～哈哈，玩得挺开心的～不说了，看照片吧～

         ... ...

人生啊，我终于又更新了。星期一开始又要上课了。第六题做出来没有？『转到第六题』 先要用简单的数学三角学原理去思考。

如图右图，卫星绕地球运动的轨道为一椭圆（为了明显，夸张了离心率），地心位于轨道椭圆的一个焦点O处，设待测量星体位于C处。因为两个卫星刚刚好相差半个周期，当一个卫星运动到轨道的近地点A时，另一个卫星恰好到达远地点B处，只要位于A点的卫星用角度测量仪测出AO和AC的夹角a，位于B点的卫星用角度测量仪测出BO和BC的夹角b。如果知道了AB，AO，就可以用三角原理计算出此时星体C与地心的距离OC。

假如这道题当成天文题来做的话，完全可以用AC来代替OC。因为星体到地球的距离实在是远远远大于卫星到地球的距离，大太多了。AO和OC的值基本相等。当然，我们在做物理题了，还是要考虑的。毕竟，如果那个星体是太阳系内的天体的话...（那也不能叫星体啊）

然后问题就来了，我们知道AO = 2R，和卫星在近地点速度，怎求AB（就是OB）呢？两个方法，一个是用开普勒第二定律，即面积定律，不过这样要用微积分了，不会；还有一个是角动量守恒。其实两个方法是一个原理。啥是角动量来着，中国高中物理貌似没有讲。这是在Rotational Dynamic里面的，区别于Linear Dynamic。角动量就是L，绕固定轴旋转的物体的顺时角动量，是它的Inertia（惯性）I，和角速度w的乘积。当作用在物体上的外torque（我真不知道这个中文怎么说）的和等于0的时候，这个叫角动量的东西就守恒了，就相等了。

在这个问题里，地球可以看作唯一对卫星作用的物体。因为卫星做椭圆运动，地球在焦点上，地球对卫星的引力时刻都经过卫星的旋转中心；所以地球对卫星的torque是0。可以理解为玩跷跷板的时候，沿着板拉不能使另一端翘起来。还有就是惯性，在Rotational Dynamic里面惯性等于物体质量和物体到旋转轴距离的平方的乘积。即I = mr²。神奇吧～

所以，设卫星在远地点到地心距离为r₂，在近地点到地心距离为r₁，根据角动量守恒，有：

L₁ = L₂；即I₁w₁ = I₂w₂；即m₁r₁² ×（v₁ / r₁）= m₂r₂² ×（v₂ / r₂）

所以： m₁r₁v₁ = m₂r₂v₂ （式一）

因为只有保守力做功，根据机械能守恒， 可以得出：E_k1 + E_p1 = E_k2 + E_p2；

所以： (1/2)m₁v₁² + m₁（GM/r₁2) r₁= (1/2)m₂v₂² + m₂（GM/r₂2) r₁ （式二）；M为地球质量，G为引力常数。

带入 r₁ = 2R；v₁² = 3GM / 4R；得到 r₂ = 6R，所以OB = 6R；AB ＝ 8R。

根据正弦定理，求出AC。在三角形AOC中用余弦定理求出OC即可。由于表达式中包含很多根号和分数，就不列出来了，反正剩下就是数学了，自己算吧。^_^

第七题：自己编的。天文社同学回答吧～

用赤道仪进行天文摄影，好的极轴是好照片的必要条件。1. 请写出三种不同的对极轴方法，简单解释即可。 2.在用漂移法对极轴时，一定要选择天赤道上的星吗？请简单说明理由。 

好吧正常点：第七题：

  一个木桶，里面有一半水。用一条长绳子把木桶悬吊起来，长绳的另一端固定在天花板上。系统静止的时候，木桶，绳子，都垂直与水平地面。1. 当木桶绕着竖直旋转轴逆时针匀速旋转时，绳子被拉直，并与竖直旋转轴成一定角度。请问木桶里的水面如何运动。2. 当木桶做逆时针匀加速圆周运动时，水面如何运动。3. 如果是逆时针匀减速圆周运动呢？

注：考虑水与木桶的摩擦；绳子长度不变；图像仅作示意用，不代表桶和水的真实运动；系统在地球上。要考虑地转偏向力也可以，试试。那个变速的时候，绳子与竖直旋转轴的夹角会变的。

这道题我是突然想出来的，貌似小学的时候在哪里看到过。我也不知道怎么做。所以大家一起做啦！

呵呵，老照片老照片，翻出来，放上来。08年的一次中国看不到的月全食。当时可是没有三脚架，手持拍摄的。而且相机最长焦距是55mm。

图片在这里～