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)