Yep - you don't need to touch matrices for this. What part of the maths are you finding hard. I guess you already know how to rotate a vector?
cos_rot# = Cos(rotation_angle#)
sin_rot# = Sin(rotation_angle#)
new_x# = (x# * cos_rot#) - (y# * sin_rot#)
new_y# = (y# * cos_rot#) + (x# * sin_rot#)