Question

A 47 degres counterclockwise rotation centered at (3,-1) transforms (2,1) into what point?

Answer 1

first, write (2,1) = (3,-1)+(-1,-2)
so, the rotation has the same effect around (3,-1) as rotating (-1,-2) around the origin.

So, use your normal transformation matrix on (-1,-2) to produce (h,k).
Then undo the translation by adding back in the (1,2) you took away first.