Exercise 23, § 4

Let $p$ be a prime number; give an example of $\mathbf{Z}$-modules $M, N$, where $N$ is finitely generated, such that $M_{(p)} \neq 0$ and $N_{(p)} \neq 0$, but $(M \otimes_{\mathbf{Z}} N)_{(p)} = 0$ (take $M = \mathbf{Q}$).