I believe this is a simple sentence. Since this sentence has one independent clause which contains one subject, the library, and a simple predicate, it's peaceful and quiet. However, this predicate has two verbs, known as a compound predicate: peaceful and quiet. This compound verb should not be confused with a compound sentence, since they contain two separate clauses. Example: I really enjoy going to the library, it always seems to be quite and peaceful at that place.
