After the quarrel, I did send a letter to scold her with a bunch of ugly words, saying that she was bored. Later, I apologized. She didn't reply to the message. What does silence mean?

It means she's still angry. Think about whether you should dump your boy. If you apologize, people won't be angry, will they? You shouldn't say a lot of ugly words when quarreling, let alone some hurtful words. You should know that a kind word warms people's hearts. A bad word is cold in three winters. It's hard for you to scold her like that. I want to solve it by apologizing. Nice try. Prepare gifts, a big meal is a must. Plus a sincere apology and a sincere guarantee. It's possible for her to say hello to you.