It turns out that scalars also share this coordinate invariance property.

事实证明，标量也具有这种坐标不变性。

We know how to multiply by a scalar.

们知道如何乘以一个标量。

When you multiply it by a scalar, or you're not changing its direction.

当你把它乘以一个标量，或者你没有改变它的方向时。

And now let's  begin the unit 1 review in earnest with vectors and scalars.

现在让们从向量和标量开始认真复习第一单元。

And Bobby, please give me some examples of scalars in physics.

鲍比, 请给举一些学中标量的子。

Like if, you know, let's go back to our kind of second grade world of just scalars.

就像，你知道的，让们回到们那种只有标量的二年级世界。

The scalar scaled up the vector. That might make sense.

标量放大矢量, 这也许是有道的。

Remember how I said that linear algebra revolves around vector edition and scalar multiplication?

还记过线性代数围绕着向量编辑和标量乘法吗？

Or it might make an intuition of where that word scalar came from.

或者它可能会直觉地知道" 标量" 这个词来自哪里。

The only variable which is the same in both  directions is change in time because change in time is a scalar.

唯一在两个方向上相同的变量是时间的变化，因为时间的变化是一个标量。

The scalar, when you multiply it, it scales up a vector.

标量, 当你乘以它时, 它会放大一个向量。

This is considered to be a scalar quantity.

这被认为是一个标量量。

The way you'll often hear this described is that linear transformations preserve the operations of vector edition and scalar multiplication.

您经常听到的描述是 线性变换保留了向量编辑和标量乘法的操作。

When we multiply it times some scalar factor.

当们将它乘以某个标量因子时。

You often think of this as being broken up into a real or " scalar" part, and then a 3d imaginary part.

您通常认为它被分解为实部或“标量” 部分，然后是 3d 虚部。

Examples of scalars are time, distance, mass, speed, volume, density, work, energy,   rotational inertia, and that's all I can think of.

标量的子有时间、距离、质量、速度、体积、密度、功、能量、动惯量，这些就是能想到的。

Or even better, what vector, if I take any arbitrary scalar-- can represent any other vector on that line?

或者更好的是，如果采用任何任意标量，那么哪个向量可以表示该行上的任何其他向量？

The distance between you and a bench, and the volume and temperature of the beverage in your cup are all described by scalars.

你和长凳之间的距离，以及你杯子里饮料的体积和温度，都是用标量来描述的。

So what happens if we take t, so some scalar, times our vector, times the vectors b minus a?

那么，如果们取 t， 即一些标量， 乘以们的向量，乘以向量 b 减去 a， 会发生什么呢？

But we just did it the first way the last time because I wanted to go from my basic definitions of scalar multiplication.

但是们上次只是用第一种方法来做，因为想从对标量乘法的基本定义开始。