After calculating the eigenvalues, I get $1040400$ and $0$. Since one of them is $0$, how do I calculate (orthogonal) matrix $U$?
$$u_i = \frac{1}{\sqrt{\lambda_i}} A v_i$$
I know there are a similar question here, but when calculation $u_1$ it's a null vector. So, I don't see how I can find $u_2$.
To find $u_2$, simply set $u_2$ to be any unit vector orthogonal to $u_1$. More generally, if a matrix with $m$ rows has $k$ non-zero singular values, then columns $u_{k+1},\dots,u_m$ are found by completing the orthonormal basis $u_1,\dots,u_k$ (by using the Gram Schmidt procedure, for instance).