a. \(\sqrt{25x^2}=100\)

\(\Leftrightarrow\sqrt{\left(5x\right)^2}=100\)

\(\Leftrightarrow\left|5x\right|=100\)

\(\Leftrightarrow\left[{}\begin{matrix}5x=100\\5x=-100\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=20\\x=-20\end{matrix}\right.\)

b. \(\left(\sqrt{3}-\sqrt{2}\right)x=\sqrt{27}-\sqrt{18}\)

\(\Leftrightarrow\left(\sqrt{3}-\sqrt{2}\right)x=\sqrt{3^2.3}-\sqrt{3^2.2}\)

\(\Leftrightarrow\left(\sqrt{3}-\sqrt{2}\right)x=3\sqrt{3}-3\sqrt{2}\)

\(\Leftrightarrow\left(\sqrt{3}-\sqrt{2}\right)x=3\left(\sqrt{3}-\sqrt{2}\right)\)

\(\Leftrightarrow x=3\)

Để \(AC\perp BD\Leftrightarrow\) ABCD là hình vuông/ hình thoi.

Mà ABCD là hình thang vuông tại A và B \(\Rightarrow\) \(AC\perp BD\) khi ABCD là hình vuông

\(\Leftrightarrow AB=BC=AD\) \(\Leftrightarrow a=b=h\)

1c

2e

3f

4b

5a

6d

31. C

32. D

33. C

34. B

35. D

36. B

37. C

38. B

39. A

40. A

41. B

42. C

43. C

44. D

45. B

46. D

47. D

48. C

49. B

50. A 

1. on

2. in

3. for

4. in

5. of

6. near

7. on

8. with

9. on

10. on

11. had left

12. had written

13. wrote

14. had broken

15. to have established 

16. have tried

17. left

18. will have had

19. does this word mean

20. Does John usually play

IV.

16. since

17. or

18. but

19. unless

20. so

V.

21. didn't make -> haven't made

22. little -> a few

23. bỏ too

24. bought -> were bought

25. builds -> will be built

1. had had

2. will have learned

3. walked

4. has been

5. went

6. finishes

7. had written

8. has finished

9. floats

10. lays

1. How long have these students worn this uniform?

2. Because your friends don't prepare for the next exam well, they will get bad marks.

3. She has written this novel for three years.

4. I wish my father didn't have to work on the weekends.

5. I wish he came there on time.

15. C

16. A

17. B

18. D

19. C

20. D

21. A

22. B

23. A

24. C

25. B