For the simplest context in which one can motivate a vector and also motivate the rules for dealing with vectors, is when you look at real space, the coordinates x and y.

对于最简单的情况,我们能用矢量,以及相关的规则来处理的,是实空间,x-y 坐标系

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You can imagine that if a vector is viewed from an angle, then its components will vary with the perspective.

你可以想象一下,如果换一个角度观察矢量,其分量会相应地发生变化

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The second issue is that the gene vector, in this case the plasmid, has to be compatible with the cells that you're trying to express the gene in.

接下来的问题是如何选择合适的基因载体,在这里用到的,质粒,必须与要用来表达基因的,受体细胞匹配

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You can deal with a vector in one of two ways.

你有两种方法来表示矢量

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You can actually take derivatives of a vector with time.

你可以直接求位矢对时间的导数

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Even though we started with a single vector, which is the position vector, we're now finding out that its derivative has to be a vector and the derivative of the derivative is also a vector.

即使我们从单个矢量出发,即位移矢量,我们现在也能得出它的导数是矢量,而且导数的导数也是一个矢量

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I think it's clear, the position of the object with respect to the ground, this vector is the same as the position of the object with respect to the plane, plus the position of the plane with respect to the ground.

我觉得很明显,物体相对于地面的位置,这个矢量等于,物体相对于平面的位置矢量,加上物体相对于地面的位置矢量

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But then, I combine i times Ax with i times Bx, because that's the vector parallel to i, with the length Ax.

然后我把 i ? Ax 和 i ? Bx 加起来,因为这是平行于 i,模长为 Ax 的矢量

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That's clear. If I add them, I'll get a vector parallel to i with lengths Ax + Bx.

这很明显 如果把他们加起来,就得到一个平行于 i,模长为 Ax + Bx 的矢量

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The typical vector is called V or A or B something with an arrow on it.

表示矢量时一般在,字母 V,A 或者 B,上面加个箭头

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It's not enough to say these are the components of the vector; you've got to tell me, "I am working with i and j, which I define in the following manner."

所以,只说"这些是某矢量的分量"是不够的,你还得告诉我,"我选取的基矢是 i 和 j,它们是这样定义的"

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That's the vector parallel to i, with length Bx.

这个是平行于 i,模长为 Bx 的矢量

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Now, when you work with components, Ax and Ay, if I didn't mention it, they are the components of the vector, you can do all your bookkeeping in terms of Ax and Ay.

当你们在计算分量 Ax 和 Ay 的时候,即使我没有说明,你们也要记得它们是矢量的分量,你们可以都用 Ax 和 Ay 的形式来表示

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If you are describing a particle with location R, the vector we use typically to locate a particle, R then R is just i times x + j times y, because you all know that's x and that's y.

如果你要描述一个位移为 R 的质点,这个矢量一般用表示质点 R 的位移,R 可表示为 i ? x + j ? y,显然你们都知道这段是 x,那段是 y

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You have to be able to get the DNA into the cell, it has to be incorporated into a vector of some sort, and the vector has to be compatible with the species and the cells that you've provided the DNA to.

你必须把整合在,某种特定载体上的DNA导入细胞,载体也必须和,受体物种,及细胞匹配

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