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Именительный (nominative) - Кто? Что?
And
Винительный (accusative) - Кого? Что?

Both cases have the same question "Что?". But maybe it isn't a problem for you.

That's correct.

3. (Кто?) Учитель (so it's nominative) проверил (Что?) задание (so it's accusative and it's a direct object).

4. (Кто?) Туристы посетили (Что?) музей.

In Russian there is...