Consider the transformation t: x=4041u−941v, y=941u+4041v a. compute the jacobian: ∂(x, y)∂(u, v)= b. the transformation is linear, which implies that it transforms lines into lines. thus, it transforms the square s: −41≤u≤41,−41≤v≤41 into a square t(s) with vertices: t(41, 41).