Cho hình lập phương ABCD.A'B'C'D'. M, N, Q lần lượt là trung điểm của BC, C'D', AA'

a) Tìm E = MN giao (ACC'). Chứng minh: E là trung điểm của MN

b) Chứng minh: QE, AC', BD' đồng quy

c) Tìm I = BD' giao (MNQ). Chứng minh: I là trọng tâm tam giác MNQ

Xét khai triển (1+x)(1+2x)(1+3x)....(1+2019x) = a₀ + a₁x + a₂x² + a₃x³ +...+ a₂₀₁₉x²⁰¹⁹. Tính S = 2a₂ + (1¹ + 2² +...+ 2019²)

1. have learned

2. didn't work / were not

3. want to pass / will study

4. sent

5. was / think / learned

6. had gone / didn't enjoy

7. did / met

8. noticed / is

9. have / had

10. revise

11. have already begun

12. think / will do

13. is / isn't

14. pass / will start

15. will go

16. can see / have become

C4: 1+2-3-4+...+97+98-99-100

=[1+2-3-4]+[5+6-7-8]+...+[97+98-99-100]

=(-4)        +    (-4)     +...+     (-4)

= (-4) . 25 = -100

LƯU Ý CÓ THỂ ĐÁNH DẤU CÁNH CÒ DƯỚI BƯỚC THỨ 2 VÀ GHI RÕ 25 SỐ (-4)...OK ^_^

1. A

2. B

3. C

4. C

5. C

6. D

7. A

1. Dickens "David Copperfield" is the most popular book

2. You should have considered our suggestion before making official decision

choose => choosing

( "by" là giới từ nên sau "by" là V_ing)

|x-1|=0

=>x-1=0

=>x=0+1

=>x=1

-13.|x|=-26

=>|x|=-26:(-13)

=>|x|=2

=>x\(\in\){-2;2}

1. In spite of the bad weather, they din't cancel the flight to tokyo

2. They still live here although air is polluted

3. She can work even though it is very noisy

4. They drove fast although the road is narrow

5. She didn't stay at the hospital in spite of her bad heart disease

6. Although I couldn't sleep during the night in spite of, I could see nothing

7. In spite of the heavy case, he carried it easily

8. In spite of difficult questions, he answered all them

9. Despite her serious illness, she doesn't see her doctor

10. Despite the strong coffee, he can drink it

1. I didn't like her though she was very kind

2. Even though she was it, she went on working

3. We drove slowly because it was snowing

4. Larry is older than Meg although she is taller than he is