Hamlet 3.4 “What Wilt Thou Do?”

Gertrude considers leaving to find Claudius, whose authority Hamlet must obey. However, Hamlet stops her, forcing her to stay and confronts her with his perception of her true nature. Hamlet, who has been feigning madness, becomes genuinely angry and potentially violent, frightening Gertrude. She cries out for help, fearing Hamlet's rash actions.

What does Hamlet's anger and rudeness signify about his mental state?

What might Hamlet do that frightens Gertrude?