  Let $f$ be a normalized holomorphic cusp form for $SL_2(\mathbb{Z})$ of
weight $k$ with $k\equiv0\bmod 4$. By the Kuznetsov trace formula for
$GL_3(\mathbb R)$, we obtain the first moment of central values of
$L(s,f\otimes \phi)$, where $\phi$ varies over Hecke-Maass cusp forms for
$SL_3(\mathbb Z)$. As an application, we obtain a non-vanishing result for
$L(1/2,f\otimes\phi)$ and show that such $f$ is determined by
$\{L(1/2,f\otimes\phi)\}$ as $\phi$ varies.
