Linearization, critical points, and equilibria

Find the critical points and linearizations of the following systems.

1. $x'=\sin(\pi y)+(x-1)^2$, $y'=y^2-y$,
2. $x'=x+y+y^2$, $y'=x$,
3. $x'=(x-1)^2+y$, $y'=x^2+y$.

The idea of critical points and linearization works in higher dimensions as well. You simply make the Jacobian matrix bigger by adding more functions and more variables. For the following system of 3 equations find the critical points and their linearizations:

Any two-dimensional non-autonomous system $x'=f(x,y,t)$, $y'=g(x,y,t)$ can be written as a three-dimensional autonomous system (three equations). Write down this autonomous system using the variables $u$, $v$, $w$.