Example of a subset of $\mathbb{R}^2$ that is closed under vector addition, but not closed under scalar multiplication? I've found several examples which are closed under scalar multiplication, but not vector addition, but I can't come up with one that is closed under vector addition, but not scalar multiplication. 

The set $\{(x,y): x\ge0, y\ge0\}$ is closed under addition, but not under scalar multiplication, since $-1\cdot(1,1)=(-1,-1)$, for example.
