Some areas of oceans are about 11 km deep. Is it because continental plates were moving away because of troughs in the middle from where new rock is formed? If so, why did it become deep? If not, what are other reasons?
The deep zones in the ocean are not where new rock is formed. The trenches are the areas where rock is subducted back into the mantle. Here's a picture to visualise it:
New rock is formed at mid ocean ridges (for example 12 in the image). Those are areas that are less deep than the rest of the ocean. This rocky plate sinks underneath another plate (either continental or oceanic) and by doing so "pulls" that plate down (for example 13 and 18 in the image). This is what causes the extreme depth of those areas.