Were you guys surprised by anything that you found when you actually printed out the final details?
当你们把最后的结论打印出来时,你们有没有对自己的发现感到惊讶
You have access to capital by those guys, these guys who are no longer there.
你能通过这些家伙进行融资,这些家伙已经不在了
You guys have been trained by your culture to define what constitutes a food.
大家都在特定的文化熏陶下,知道了什么构成了食品
And please sign in, by the way, guys, before you leave.
顺便说一下,同学们在离开之前请签名。
By the way, Mr. Newton did not have math guys he could go to.
顺便说一下,牛顿先生可没有数学外援
So rather than go through this again a whole third time, I've gone through it once in quantities and once in prices, I'm going to get you guys to do it this time by having you do it on a homework assignment.
与其从头到尾再做第三遍,我已经从产量和价格角度从头到尾做过了,我将让你们自己,在家庭作业中完成这个工作
Now, that's a very important point, because why in the world would you give a shield of the kind I am describing, for a man to defend himself, if you imagine him standing by himself anywhere, if you imagine him any distance from the rest of the guys fighting alongside of him.
这点非常关键,那就是到底为什么要将,这样一种盾牌,给士兵们使用,想象一下这个场景,这个士兵在战场的某个角落孤军奋战,与其它友军士兵相隔甚远
By the way, when you guys do this, did anybody notice prime?
顺便问一下,你们刚才听课的时候,有人注意要加撇吗
That would come by saying, "I'm taking i times Ax + j times Ay + i times Bx + j times By, " and I'm trying to add all these guys.
那就这样做,"i ? Ax + j ? Ay + i ? Bx + j ? By",然后把它们都加起来
If you want to add two vectors, you can add the arrows by the rule I gave you or just add the components of x of the two guys to get the component of the sum and likewise for the y.
如果要把两个矢量相加,你可以用我教给你们的箭头相接的方法,或者就将二者的 x 分量相加,得到和矢量的 x 分量,y 方向也是这样
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