I have an amplitude damping channel, denoted as a superoperator $\mathcal{E}$ with operator elements

\begin{matrix}
		E_1=\begin{pmatrix}
		1 &  0 \\ 
		0 &  \sqrt{1-r} 
		\end{pmatrix},\quad
		E_2=\begin{pmatrix}
		0 &  \sqrt{r} \\ 
		0 &  0 
		\end{pmatrix}
		\end{matrix}
I am confused that how to explicitly obtain the $\mathcal{E}^{\otimes 2}$ in matrix form?	

Also, I am trying to understand what is $\mathcal{E}^{\otimes 2}(\rho)$, where $\rho=1/2|00\rangle\langle 00|+1/2|11\rangle\langle 11|$?