Alright. I was looking into a 2D rotation matrix and there are two equations: one is through the transformation of the component of p (always with respect to x,y), x,y into x',y' and the other is through the transformation of the unit vectors i,j into i',j'. In a sense 1 is passive the other is an active transformation. I do understand the difference between the two, but my question is that why do we get the different matrices if when we derive them, we do so with a clockwise orientation? Hope its clear, If not--I'd be happy to clarify.