This is your first lecture in which you have the option of either staying awake or dozing off for a little bit. If you stay awake, then your Academics will increase; if you choose to doze off, then there's a chance your condition will improve. The game will automatically advance to the Dark Hour.
Yukari will give you a short sword before leaving your room. When you gain control of your character, run up the stairs until you encounter another cutscene. After this one, you'll be thrown into a battle with two Cowardly Mayas. Use Orpheus' Bash skill to finish them in one hit each to finish the battle. You will visit the Velvet Room again and Igor will mention about the connection of your Social Links and the power of your Personas.
