Actually, the view of vectors we take nowadays is that vectors are associated with a pair of numbers which, on the rotation of axes, transform like this.

实际上,今天我们讲矢量所用的观点是,矢量是和一组坐标值相对应的,在坐标轴旋转的过程中像这样变换

耶鲁公开课 - 基础物理课程节选

How do the components of A in the new rotated coordinate system relate to the components of the old coordinate system?

在旋转后的新坐标系中 A 的分量,和原始坐标系中 A 的分量有什么关联呢

耶鲁公开课 - 基础物理课程节选