It's too bad that Q isn't a whiz with linear algebra (or matrix multiplications as you put it). Rotations and scaling are linear transformations. For the following examples, assume that A is a 2xn matrix (that is 2 columns and n rows; n is the number of points that you're dealing with).
Rotation by an angle t:
A' = A * [ [cos t, -sin t][sin t, cos t] ];
Scaling by a factor of x:
A' = A * [ [x, 0][0, x] ];
Translation by dx in the x direction and dy in the y direction
(not actually linear transform, but easily accomplished with matricies
A' = A + [ [dx, dy] ]; ( add dx to each value in the first column and
+dy to each in the second column)
I would help you with skew, but I don't know *how* you want to accomplish this. In colloquial terms, I'd imagine a stretch of some description, but I don't know what kind of parameters you've got.
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For all of us waiting, your kingdom will come
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