Does rotation of a rectangle keep it rectangular? If I rotate a rectangle by 45°, does it stay rectangular or become something else? I mean do 90° angles stay 90°?
I am asking this question because I have some results where the rotated rectangle becomes not so rectangular ... I think I have a problem.
Problem: I think the problem comes from scaling.... I draw the resulting data after rotation in another image, and I have got the rectangle correctly rotated. Maybe it is because I used imagesc to draw the background or axis image in MATLAB...?

If rectangles are rigidly rotated all lengths remain same. It looks like a parallelogram, it is due to unequal scaling factor in SF x- and y-. 
In a proper rotation/translation, it is just as in a transparent polyester sheet / view graph is displaced on the table and  nothing happens relatively between line segments by scaling or distortion.
$ x1 = x \cos t - y \sin t ; \,  y1 = SF (x  \sin t + y  \cos t)  $ 
Aspect Ratio is to be $1$ before and after rotation.
