homework and exercises - Would this box on the floor rotate based on friction?

There is a floor that friction is proportional to its velocity (like $F=-kv$) and there is a box with its width as $l$ and its height as $h$. (you may assume that $l$ is longer than $h$). It is on the floor with the initial velocity $v$. Then, if $v$ is big, I think it would rotate. But I don't know how to analyze this situation as differential equation.

This figure shows the situation it rotate as the $\angle \theta$. But, as the initial time, $\theta$ is $0$ so thus I think its friction would not be exerted at the left-bottom corner. So it will be different with this figure.

If there is no floor, the rotate pivot is just the center of mass I think. But there is a floor. It makes me crazy.