A solid ellipsoid $E$ which contains $(1,2)$ is transformed to a region $T(A)$ using $T(x,y) = (x^2 +y^2, xy)$. Approximate the volume of $B$ if the volume of $A$ is $0.1$.
I have absolutely no idea where to begin. My first idea is to use the determinant, but $T$ is non-square. I am completely lost... any guidance is greatly appreciated.