If they are annuals, they are dead and will not come back. Annual means they complete their entire life cycle in one year. They just need to be pulled out.
But they look like they may be chrysanthemums to me. In that case they are perennials - plants that return year after year from the roots.
I think I would give them some water for a few days and see if you see any signs of new growth at the base. If you do, then yes, cutting back the dead top growth is a good idea to let the light get to the new leaves.
But, as greene said above, you really should also check with the apartment manager before you mess with the plants.