Определите время:
A letter is being written by her.
A book was being written by him.
By whom was this letter written?

В предложениях употреблены разные времена английского глагола в Passive Voice.

1. A letter is being written by her.
Время: Present Continuous Passive — настоящее длительное время в страдательном залоге.

Формула: am / is / are + being + V3
Перевод: «Письмо пишется ею» / «Она сейчас пишет письмо».

2. A book was being written by him.
Время: Past Continuous Passive — прошедшее длительное время в страдательном залоге.

Формула: was / were + being + V3
Перевод: «Книга писалась им» / «Он писал книгу в тот момент».

3. By whom was this letter written?
Время: Past Simple Passive — прошедшее простое время в страдательном залоге.

Формула: was / were + V3
Перевод: «Кем было написано это письмо?»

Итак, ответы:

A letter is being written by her. — Present Continuous Passive.
A book was being written by him. — Past Continuous Passive.
By whom was this letter written? — Past Simple Passive.