Let $M$ be a positively graded finitely generated module over a positively graded commutative ring $R$. Assume that $R_0$ is a local ring with maximal ideal $m_0$. Let $d$ be the Krull dimension of $M$. In the book "Local cohomology: An algebraic introduction with geometric application" by M.P.Brodmann and R.Y.Sharp, the authors claim that if $d=0$ then the set of associated prime ideals of $M$ is $\lbrace m_0 \oplus R_+ \rbrace$, and therefore there exists a $t\in \mathbb{N}$ such that $R_{+}^{t}M=0$.

My question is :

Why do we have Ass(M)= $\lbrace m_0 \oplus R_+ \rbrace$?

Why does this imply $R_{+}^{t}M=0$ for some $t\in \mathbb{N}$?