Near what points $(r,s)$ can the transformation
$x = r^2 + 2s$
$y = s^2 - 2r$
be solved for $r$ and $s$ in terms of $x$ and $y$
Find $\frac{\delta r}{\delta x} , \frac{\delta r}{\delta y}, \frac{\delta s}{\delta x}, \frac{\delta s}{\delta y}$ when $(x,y,r,s)=(0,0,0,0)$
2. The Jacobian of the transformation $(r,s) \mapsto (r^2+2s, s^2 - 2r)$ is $4(rs+1)$ which vanishes iff $rs=-1$....