a) \(A=\dfrac{1}{3}-\dfrac{3}{4}-\left(-\dfrac{3}{5}\right)+\dfrac{1}{72}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{15}\)

\(=\dfrac{1}{3}-\dfrac{3}{4}+\dfrac{3}{5}+\dfrac{1}{72}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{15}\)

\(=\left(\dfrac{1}{3}+\dfrac{3}{5}+\dfrac{1}{15}\right)-\left(\dfrac{3}{4}+\dfrac{2}{9}+\dfrac{1}{36}\right)+\dfrac{1}{72}\)

\(=\left(\dfrac{5}{15}+\dfrac{9}{15}+\dfrac{1}{15}\right)-\left(\dfrac{27}{36}+\dfrac{8}{36}+\dfrac{1}{36}\right)+\dfrac{1}{72}\)

\(=1-1+\dfrac{1}{72}\)

\(=0+\dfrac{1}{72}=\dfrac{1}{72}\)

b) \(B=\dfrac{1}{5}-\dfrac{3}{7}+\dfrac{5}{9}-\dfrac{2}{9}+\dfrac{7}{13}-\dfrac{2}{11}-\dfrac{5}{9}+\dfrac{3}{7}-\dfrac{1}{5}\)

\(=\left(\dfrac{1}{5}-\dfrac{1}{5}\right)+\left(-\dfrac{3}{7}+\dfrac{3}{7}\right)+\left(\dfrac{5}{9}-\dfrac{5}{9}\right)-\left(\dfrac{2}{9}-\dfrac{7}{13}+\dfrac{2}{11}\right)\)

\(=0+0+0-\left(\dfrac{286}{1287}-\dfrac{693}{1287}+\dfrac{234}{1287}\right)\)

\(=-\left(-\dfrac{173}{1287}\right)\)

\(=\dfrac{173}{1287}\)

c) \(C=\dfrac{1}{100}-\dfrac{1}{100.99}-\dfrac{1}{99.98}-.....-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)

\(=\dfrac{1}{100}-\left(\dfrac{1}{100.99}+\dfrac{1}{99.98}+\dfrac{1}{98.97}+...+\dfrac{1}{3.2}+\dfrac{1}{2.1}\right)\)

\(=\dfrac{1}{100}-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{97.98}+\dfrac{1}{98.99}+\dfrac{1}{99.100}\right)\)

\(=\dfrac{1}{100}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{97}-\dfrac{1}{98}+\dfrac{1}{98}-\dfrac{1}{99}+\dfrac{1}{99}-\dfrac{1}{100}\right)\)

\(=\dfrac{1}{100}-\left(1-\dfrac{1}{100}\right)\)

\(=\dfrac{-49}{50}\)

Kẻ đường chéo AC.

\(\Delta ABC\) có MA = MB, NB = NC

\(\Rightarrow\) MN là đường trung bình của \(\Delta ABC\)

\(\Rightarrow\) MN // AC và \(MN=\dfrac{1}{2}AC\) (1)

\(\Delta ADC\) có FD = FA, ED = EC

\(\Rightarrow\) EF là đường trung bình của \(\Delta ADC\)

\(\Rightarrow\) EF // AC và \(EF=\dfrac{1}{2}AC\) (2)

Từ (1) và (2) \(\Rightarrow\) MN // EF, MN = EF \(\Rightarrow\) tứ giác MNEF là hình bình hành (đpcm).

\(M=x^3-3xy\left(x-y\right)-y^3-x^2+2xy-y^2\)

\(=x^3-3x^2y+3xy^2-y^3-\left(x^2-2xy+y^2\right)\)

\(=\left(x-y\right)^3-\left(x-y\right)^2\)

Có: x - y = 11 \(\Rightarrow\left(x-y\right)^3-\left(x-y\right)^2=11^3-11^2=1210\)

Vậy M = 1210

WORD FORM:

1. Many ___visitors_ (visit) come to DCM's Mausoleum every year

2. Everyone was very (friend) friendly to me

3. He was always guided by (religion) religious belief

4. You can't be (depend) dependent on your parents

5. The (nation) national language in Malaysia is Bahasa Malaysia

6. What is the main language of (instruct) instruction at that school?

7. My home village are very quiet and (peace) peaceful.

8. She plays the piano (beauty) beautifully.

9. We were impressed by the ( beautiful) beauty of the city

10. I don't like Mai because her (friend) friendliness makes me unhappy

11. She was really (impress) impressed by the beauty of Hanoi

12. In some countries, military service is (compel) compulsory.

13. In Malaysia, (educate) education is free

14. First (impress) impression can be misleading

15. The editor welcome (correspond) correspondence

from readers on any subject

16. By the age of eighteen he was completely (depend) independent

of his parents

17. Many parents opposed the (divide) division of the classes into different sets

18. English and French are canada's (office) offical languages

19. America's (industry) production fell for the fourth successive month

20. I like the constant (compel) compulsory with students from other classes

21. How can we make the subject more (interest) interesting to young people?

22. Islam is one of the great world (religious) religion.

23.There was an (interest) interestingcartoon on Disney Channel last night

24. He has been the BBC's political ( correspond) correspondent for many years

25. he left the company for a (vary) variety of reasons

26. One of those boys was not pleased with the (divide) division of their father's money

27. The list of their achivements is pretty (impress) impressive

28. We need to get more young people (interest) interested in the sport

29. The sights of the city never fail to (impress) impress tourists

30. English, Tamil and Chinese are (wide) widely spoken in Malaysia

31. I don't have time to take you to visit place of (interesting) interest because I'm so busy

32. English is an (nation) national language

33. I can't stand such (friend) friend here

34. The festival is (official) office held in Hung King Temple

35. We need the (compel) compelation of this attendance

36. Angkor Wat used to be a (religion) religious center

37. The internet has helped students study more (depend) dependent.

38. It was (friend) unfriendly that she left without saying a word to us

39. Quebec wanted some forms of (separate) separation from the rest of Canada

40. The garden is (beauty) beautiful with trees and flowers by Mrs. Green

41. This film has been (nation) national since 1975

42. There will be some (meet) meeting on this street

43. She considered as a (hero) heroes because of saving the baby from drowning

44. Some young people today have a very strang (appear) appearance.

45. Her clothes look very mmodern and (fashion) fashionable.

46. Many (write) writers are normally inspired with beauty

47. What a (color ) colorful T-shirt !

48. His (appear ) appearence made me surprised

49. Many teenagers are now (fashion) fashionably dressed

50 . Is Kuala Lumpur (differ) different from Hanoi?

51. In the 18 th century, jeans cloth was (complete) completed made from cloth

52. These clothes are attractive but entirely (practice) practiced.

53. Many people enjoy the pleasure and (convenient) convenience of living downtown

54. TCS is one of the most well-known (music) musicals in VN

55. I like wearing loose (comfort) comfortable clothes

56. What type os clothing is (need) needed for survival at these situations?

57. You've made your parents very (pride) proud.

58. It's not (fashion) unfashionable to wear short skirts at the moment

59. He needs all the support and (encourage) encouragement​ he can get

60. Don't you belive in (equal) equality between man and women?

61. Nguyen Du is a famous (poetry) poet

62. He's a leading (design) designer of our company

63. Schools (nation) national are experiencing a shortage of teachers

64. Our production must be (modern) modernized.

65. In (conclude) conclusion, you are wrong

66. you must (economy) economise money and labor by recycling everything used

67. It's too (convenience) convenient to call anyone at nightmoney and labor by recycling everything used

68. Do you (occasion) occasionally meet each other after leaving school?

69. Many designers took (inspire) inspiration from Vn's ethnic minorities

70. We can see many (advertise) advertisement on Tv every day

71. X and Y are the two (know) known values in this exercise

72. George's (fond) fund for pink clothes was well-known

73. I'm thankful to my teacher who gives me a lot of (courage) encouragement.

74. We need to (good) better our standards of life

75. You have (bad) the situation

76. It's (convenience) convenient for me to have no car to work

77. What is your favorite type of (cloth) clothing?

78. These shoes look very smart but they are terribly (comfort) confortable.

79. Some designers have (modern) modernized the aodai by printing lines of poetry on it

80. people crowded the streets on national day to watch (color) colorful parades

81. Banyan trees (symbol) symbolize the Vnmese country

82. They choose that car because it is (economy)economic

83. She always spends her money (economy) economical

84.she runs very (fast) fast into her house

85. What (exact) exactly did the examiner ask you?

86. We (hurry) hurried gathered our things and ran to bus stop

87. Our school has a lot of (qualify) qualification teachers

Từ cuộc đấu tranh ngoại giao sau cách mạng Tháng Tám năm 1945, bài học kinh nghiệm được rút ra cho cuộc đấu tranh bảo vệ chủ quyền Tổ quốc hiện nay là

A. Nhân nhượng với kẻ thù 

B. Luôn mềm dẻo trong đấu tranh

C. Linh hoạt, mềm dẻo, khôn khéo nhưng cương quyết giữ vững độc lập chính quyền lãnh thổ

D. Cương quyết trong đấu tranh

Ta có: \(\widehat{M} + \widehat{N} + \widehat{E} + \widehat{F} = 360^o\) (tổng các góc của tứ giác)

\(\Rightarrow\) \(\widehat{E} + \widehat{F} = 360^o - (\widehat{M} + \widehat{N})\)

\(\Rightarrow\) \(\widehat{E} + \widehat{F} = 360^o - (100^o+120^o)\)

\(\Rightarrow\) \(\widehat{E} + \widehat{F} = 140^o\)

mà \(\widehat{E} - \widehat{F} = 20^o\)

\(\Rightarrow\) \(2​\widehat{F} = 120^o\)

\(\Rightarrow\) \(​\widehat{F} = 60^o\)

\(\Rightarrow\) \(​\widehat{E} = 20^o + \widehat{F} = 20^o + 60^o = 80^o\)

Vậy \(\widehat{E} = 80^o, \widehat{F} = 60^o\)

a) Kẻ đoạn thẳng AC.
Ta có: AB // CD (ABCD là hình thang)
Xét \(\Delta ABC\) và \(\Delta DCA\), có:
\(\widehat{BAC} = \widehat{ACD}\) (hai góc so le trong, AB//CD)

AC là cạnh chung

\(\widehat{DAC} = \widehat{BCA}\) (hai góc so le trong, AD // BC)

Vậy \(\Delta ABC=\Delta CDA\) (g.c.g)
\(\Rightarrow AD=BC;AB=CD\) (ĐPCM)

b) Xét \(\Delta ADC\) và \(\Delta CBA\), có:
AB = CD (gt)
\(\widehat{BAC} = \widehat{ACD}\) ((hai góc so le trong, AB//CD)

AC là cạnh chung
\(\Rightarrow\Delta ADC=\Delta CBA\) (c.g.c)

\(\Rightarrow\) \(\widehat{DAC} = \widehat{BCA}\) (hai góc tương ứng), mà 2 góc này ở vị trí so le trong
\(\Rightarrow\) AD // BC

Ta có: \(\Delta ADC=\Delta CBA\) \(\Rightarrow\) AD = BC (hai cạnh tương ứng)
Vậy AD // BC, AD = BC (đpcm)