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 $\rho=1/2|00\rangle\langle 00|+1/2|11\rangle\langle 11|$?