Number of equivalence classes in $P$
Suppose that $L_1 \in \mathsf{P}$ and $L_2$ is non-trivial. Pick $y \in L_2$ and $z \notin L_2$ arbitrary. The following is a polynomial time reduction from $L_1$ to $L_2$:


Input: $x$.
Check whether $x \in L_1$.
If so, output $y$.
Otherwise, output $z$.


This runs in polynomial time since $L_1 \in \mathsf{P}$.