7  haven't seen/saw/was taking

9 meet

11 nagging/trying

12 have been cleaning/haven't finished

13 have......done/met

14 telling/get

15 to use

26. he promised to tell her the truth by the end of the week.

27. one of my job was to supply the village with water.

28. More and more young people are doing volunteer work abroad. 

29. The goal in education is to eradicate racism.

30. When I got to the hospital, they were waiting in the waiting room.

Câu 6:

a: Gọi M là trung điểm của BC

\(AM=2a\cdot\dfrac{\sqrt{3}}{2}=a\sqrt{3}\)

\(\left|\overrightarrow{AB}+\overrightarrow{AC}\right|=2\cdot AM=2a\sqrt{3}\)

b: 

\(AG=GB=GC=\dfrac{2}{3}\cdot a\sqrt{3}=\dfrac{2a\sqrt{3}}{3}\)

\(\left(\overrightarrow{AB}-\overrightarrow{GC}\right)^2=AB^2+GC^2-2\cdot\overrightarrow{AB}\cdot\overrightarrow{GC}\)

\(=4a^2+\dfrac{4}{9}\cdot3\cdot a^2-2\cdot\overrightarrow{GC}\left(\overrightarrow{GB}-\overrightarrow{GA}\right)\)

\(=AB^2+GC^2-2\cdot\overrightarrow{GC}\cdot\left(\overrightarrow{GB}-\overrightarrow{GA}\right)\)

\(=\dfrac{16}{3}a^2-2\cdot\overrightarrow{GC}\cdot\overrightarrow{GB}+2\cdot\overrightarrow{GC}\cdot\overrightarrow{GA}\)

\(=\dfrac{16}{3}a^2-2\cdot GC\cdot GB\cdot cos120+2\cdot GC\cdot GA\cdot cos120\)

=16/3a^2

=>\(\left|\overrightarrow{AB}-\overrightarrow{GC}\right|=\dfrac{4a}{\sqrt{3}}\)