De Rham cohomology of the half plane

Question

Maybe this is a basic question, but I am confused. If I consider $M=\{x\in \mathbb{R}^2: x_1>0\}$. We have that the De Rham cohomology of M is $H^0(M)=\mathbb{R}$, because M is connected, but what about $H^p(M)$ with $p=1,2$?