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1-now – Present Continuous (Don't disturb him. He is doing his homework now)
2 at the moment - Present Continuous (They are playing chess at the moment)
3 in 1945 – Past Simple (World War II finished in 1945.)
4 the other day – Past Simple (We discussed that problem the other day.)
5 last week - Past Simple (I bought a new computer last week)
6 this week – Present Perfect (Mary has written a lot of letters to her friends this week.)
7 next week – Present Simple (My father goes to London next week.);
                        Present Continuous (My father is going to London next week.) 
                         Future Simple (My father will go to London next week.)
8 already - Present Perfect (She has already seen this film)
9 yet - Present Perfect (We have not been to the Hermitage yet.)
10 the day before yesterday – Past Simple (I took the book from the library the day before yesterday)

Hi, John. 
I am very glad to hear from you again. I have not written to you for ages, sorry. Here I am in Finland . The weather here is snow and windy. You wouldn't believe, but yesterday I went to an exhibition of photographs in the museum. I always wanted to visit this exhibition, because I wanted to get acquainted with the works of famous photographers. You know that I am fond of photography and I want to do it professionally, so I really liked the exhibition. 
It’s all for me for today. I have to go to the swimming pool now.
Write soon.
I am always pleased with your letters. 
Best regards to your family and friends. 
Yours,  
Nick