c a c a b

C A C A B

\(\left\{{}\begin{matrix}\overrightarrow{GA}+\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD}=0\\\overrightarrow{G_0B}+\overrightarrow{G_0C}+\overrightarrow{G_0D}=0\end{matrix}\right.\)

\(\overrightarrow{GA}+\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD}=\overrightarrow{0}\)

\(\Leftrightarrow\left(\overrightarrow{GG_0}+\overrightarrow{G_0A}\right)+\left(\overrightarrow{GG_0}+\overrightarrow{G_0B}\right)+\left(\overrightarrow{GG_0}+\overrightarrow{G_0C}\right)+\left(\overrightarrow{GG_0}+\overrightarrow{G_0D}\right)=\overrightarrow{0}\)

\(\Leftrightarrow4\overrightarrow{GG_0}+\overrightarrow{G_0A}+\left(\overrightarrow{G_0B}+\overrightarrow{G_0C}+\overrightarrow{G_0D}\right)=\overrightarrow{0}\)

\(\Rightarrow\overrightarrow{AG_0}=4\overrightarrow{GG_0}\)

\(\Rightarrow\overrightarrow{AG}+\overrightarrow{GG_0}=4\overrightarrow{GG_0}\)

\(\Rightarrow\overrightarrow{AG}=3\overrightarrow{GG_0}\)

\(\Rightarrow\overrightarrow{GA}=-3\overrightarrow{GG_0}\)

Câu 31: 

PT: \(CH_2=CH_2+H_2O\underrightarrow{t^o,xt}CH_3CH_2OH\)

→ Đáp án: A

Câu 32:

Ta có: \(n_{CO_2}=\dfrac{5,6}{22,4}=0,25\left(mol\right)\)

\(n_X=\dfrac{1,12}{22,4}=0,05\left(mol\right)\)

Gọi CTPT của X là C_nH_2n.

\(\Rightarrow n=\dfrac{n_{CO_2}}{n_X}=5\)

Vậy: X là C₅H_10.

→ Đáp án: D

30.

\(V_{\left(O;\dfrac{3}{4}\right)}\left(M\right)=M_1\Rightarrow\left\{{}\begin{matrix}x_1=\dfrac{3}{4}.4=3\\y_1=\dfrac{3}{4}.1=\dfrac{3}{4}\end{matrix}\right.\)

\(Q_{\left(O;-90^0\right)}\left(M_1\right)=M'\Rightarrow\left\{{}\begin{matrix}x'=y_1=\dfrac{3}{4}\\y'=-x_1=-3\end{matrix}\right.\)

\(\Rightarrow M'\left(\dfrac{3}{4};-3\right)\)

31.

\(cos\dfrac{x}{2}=-\dfrac{\sqrt{3}}{2}\Rightarrow\dfrac{x}{2}=\pm\dfrac{5\pi}{6}+k2\pi\)

\(\Rightarrow x=\pm\dfrac{5\pi}{3}+k4\pi\)

Nghiệm dương nhỏ nhất \(x=\dfrac{5\pi}{3}\Rightarrow a+b=5+3=8\)

Câu 9:

\(94n_{C_6H_5OH}+46n_{C_2H_5OH}=13,04\left(g\right)\left(1\right)\)

PT: \(C_6H_5OH+Na\rightarrow C_6H_5ONa+\dfrac{1}{2}H_2\)

\(C_2H_5OH+Na\rightarrow C_2H_5ONa+\dfrac{1}{2}H_2\)

Theo PT: \(n_{H_2}=\dfrac{1}{2}n_{C_6H_5OH}+\dfrac{1}{2}n_{C_2H_5OH}=\dfrac{2,24}{22,4}=0,1\left(mol\right)\left(2\right)\)

Từ (1) và (2) \(\Rightarrow\left\{{}\begin{matrix}n_{C_6H_5OH}=0,08\left(mol\right)\\n_{C_2H_5OH}=0,12\left(mol\right)\end{matrix}\right.\)

\(\Rightarrow\%n_{C_2H_5OH}=\dfrac{0,12}{0,12+0,08}.100\%=60\%\)

Đáp án: B

Câu 31:

Ta có: m _{tinh bột} = 1000.80% = 800 (kg) \(\Rightarrow n_{\left(C_6H_{10}O_5\right)_n}=\dfrac{800}{162n}=\dfrac{400}{81n}\left(kmol\right)\)

PT: \(\left(C_6H_{10}O_5\right)_n+nH_2O\underrightarrow{H^+,t^o}nC_6H_{12}O_6\)

\(C_6H_{12}O_6\underrightarrow{t^o,xt}2C_2H_5OH+2CO_2\)

\(\Rightarrow n_{C_2H_5OH\left(LT\right)}=2n_{C_6H_{12}O_6}=2n.n_{\left(C_6H_{10}O_5\right)_n}=\dfrac{800}{81}\left(kmol\right)\)

Mà: H = 70% \(\Rightarrow n_{C_2H_5OH\left(TT\right)}=\dfrac{800}{81}.70\%=\dfrac{560}{81}\left(kmol\right)\)

\(\Rightarrow m_{C_2H_5OH\left(TT\right)}=\dfrac{560}{81}.46=\dfrac{25760}{81}\left(kg\right)\)

\(\Rightarrow V_{C_2H_5OH}=\dfrac{\dfrac{25760}{81}}{0,8}=\dfrac{32200}{81}\left(l\right)\)

\(\Rightarrow V_{C_2H_5OH\left(60^o\right)}=\dfrac{\dfrac{32200}{81}}{0,6}\approx662,55\left(l\right)\)

Đáp án: A

Lời giải:

$\widehat{M_1}-\widehat{M_2}=\widehat{N_1}-\widehat{N_2}(1)$

$\widehat{M_1}+\widehat{M_2}=\widehat{N_1}+\widehat{N_2}(2)$ (cùng bằng $180^0$)

Lấy $(1)+(2)$ và thu gọn thì $\widehat{M_1}=\widehat{N_1}$
Mà 2 góc này ở vị trí so le trong nên $m\parallel n$

31.

\(y'=4x^3+1\)

Tiếp tuyến vuông góc với \(d\) nên có hệ số góc \(k=5\)

Gọi hoành độ tiếp điểm là \(x_0\Rightarrow4x_0^3+1=5\Rightarrow x_0^3=1\)

\(\Rightarrow x_0=1\Rightarrow y_0=2\)

Phương trình: \(y=5\left(x-1\right)+2\Leftrightarrow y=5x-3\)

33.

Vận tốc của chất điểm: \(v\left(t\right)=S'\left(t\right)=5-6t\)

\(v\left(t\right)=3\Rightarrow5-6t=3\Rightarrow t=\dfrac{1}{3}\)

\(\Rightarrow S=5.\dfrac{1}{3}-3.\left(\dfrac{1}{3}\right)^2=1,33\left(m\right)\)