Can we multiply anything by anything?
我们可以把任意两个相乘吗？
We multiply our options speed-wise with him.
我们在挑选速度型选手时有多个选择。
Once we multiply it by a very large number n, it becomes very much greater than kT.
一旦我用一个很大的n与它相乘，它就会变得比kT大得多。
In other words, when we multiply these functions, we get a function of the sum of those arguments.
换句话说，当我们把函数乘起来的时候，我们得到一个变量相加之后的函数。
But it's immediately apparent that t these are just going to cancel when we multiply this by t.
但是很明显，当我们将它乘以，这些会被消掉。
We multiply the two together and we get the expected return on a project given the level of risk.
我们将两者相乘，我们得到了可预见的在特定风险下在某项目上的附带效果。
OK, let's check. If we multiply this with a vector, Well, maybe I should do that. Let me write it on the board.
好，检查一下，如果我们把它和向量相乘，呃，我要不要写一下。我还是写在黑板上吧。
There are two ways that we multiply vectors and one is called the "dot product" often also called the scalar product.
矢量乘法有两种,一种叫做“点积“,通常也被叫作“数量积
Now we can multiply frequencies by integer values. But how can we multiply our frequency by fractional values or divide it?
现在我们可以倍增整数频率，但是我们如何以分数倍增频率，或者分频呢？
Well, the first thing it means before we multiply two vectors, let's start multiplying a vector with itself That's probably easier.
我们来看它的第一个意义，在我们用两个，不一样的向量相乘之前，我们先看一个向量和它本身的点积。
So if we want to talk about the volume of that, we just talk about the surface area, which is 4 pi r squared, and we multiply that by the thickness d r.
如果我们要讨论它的体积，我们要用的是表面面积，也就是4πr的平方，乘以厚度dr
When we multiply tiny pieces of time with small increments of daily effort, we too will find wecan accomplish magenificent things. We can change the world.
当我们把时间的碎片叠加，再加上每天的一点努力，我们们会发现我们也能成就辉煌。我们也能改变这个世界。
After all, when we lie to ourselves and to others, we multiply a thousand fold the inherent difficulties we have trying to determine what is actually going on inside us and around us.
毕竟，当我们自欺和欺人的时候，我们会使得包围着我们，令我们尝试去决定什么是确实的在我们自身内部和周围发生的固有困难在不断的倍增。
And the definition, actually, is we split the region into lots of tiny little pieces, we multiply the value of a function at the point times the area of a little piece and we sum that everywhere.
至于定义嘛，实际上，就是把区域分割成许多小区域，再把一点的函数值乘以那个小区域的面积，然后对乘积求和。
And so we might need to work out various, more complicated, formulas here, where we multiply the pain times its duration and take into account its intensity, get the sheer quantity of pain that way.
我们需要编制出各种，更复杂的公式，以便增加痛苦的倍数，延续时间，还要考虑痛苦的强度，获得痛苦的纯量。
How do we do that correction? When I first tried this, I thought, fine I'll multiply by 365/60, but I forgot this is a leap year.
我们如何进行修正呢？我第一次尝试的时候，我想，好吧我乘以365/60，但是我忘这是闰年。
Remember that we need to multiply it by the volume here, the volume of some sphere we've defined.
记住我们需要把它乘以体积，乘以某一个我们已定义的球体的体积。
We can also multiply out the expected defects per iteration by the number of remaining iterations and then by the average defect resolution effort.
我们还能够通过余下的迭代的数量和平均的缺陷分辨工作来增加每个迭代的预期缺陷。
Add, multiply, cosine, etc., can be combined to generate any mathematical equation we can think of.
加、乘、余弦等的相互组合能产生任何我们可以想到的数学方程。
Reconstruction after disasters is almost always much slower than expectations, mainly because we fail to grasp how difficulties interact and multiply.
灾害重建工作的进展速度一般比预期的要慢得多，这主要是因为我们不知道各种困难如何相互作用和成倍增加。
Today we are going to learn how to multiply two Numbers together.
今天我们来学习如何将两数相乘。
Since it is not possible to sum target fields into another target field, we need to sum and multiply the source Price fields into the target Amount field. The XPath expression looks like this.
因为不可能将目标字段的和作为另一个目标字段的值，所以我们需要求和，并乘以源price字段，作为目标amount字段的值。
So you take six thousand jobs and you multiply that at least by three in a family, you are talking about 18,000 folks that we probably won't see in the shopping center.
如果裁掉6千份工作，一个家庭至少乘以3的话，那可就是有一万八千多人不会来我们的购物中心了。
So, the number of nuclei, 119 if we were to sit and count these as well, is 119. So, we'll multiply that by just pi, r squared, to get that cross-section, and divide all of that by 1 .
如果你们数的话，原子核的数是，我们用它乘以πr的平方，得到横截面积，除以1。
What do you say we go back to my room and do some math: Add a bed, subtract our clothes, divide your legs, and multiply?
和我去我房间做数学怎么样：加一张床，减去我们的衣服，除去你的腿，然后相乘。
It wants to grow and multiply, as we do, but it doesn't know how to stop.
它总是要生长繁殖，正如我们，但是它不知道如何停止。
OK, now we know how to multiply matrices.
好，现在我们知道怎么把两个矩阵相乘了。
But remember that we need to multiply it by the volume here, the volume of some sphere we've defined.
但记住我们需要把它乘以体积，乘以一个我们定义的壳层的体积。
Let's say we have a 4x4 matrix that we want to multiply with a vector (a 4x1 matrix).
假设有一个4x4的矩阵，我们希望将其与另外一个4x1的向量进行乘法操作。
Let's say we have a 4x4 matrix that we want to multiply with a vector (a 4x1 matrix).
假设有一个4x4的矩阵，我们希望将其与另外一个4x1的向量进行乘法操作。
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