220 câu trắc nghiệm tổng hợp Toán cao cấp A2 có đáp án - Phần 9

$$\mathrm{I}=\ln (2+{\mathrm{e}}^{\mathrm{x}})+\mathrm{C}$$

$$\mathrm{I}=2\ln (2+{\mathrm{e}}^{\mathrm{x}})+\mathrm{C}$$

$$\mathrm{I}=-2\ln (2+{\mathrm{e}}^{\mathrm{x}})+\mathrm{C}$$

$$\mathrm{I}=-\ln (2+{\mathrm{e}}^{\mathrm{x}})+\mathrm{C}$$

$$\mathrm{I}=\frac{2\pi }{3}-\frac{\sqrt{3}}{2}$$

$$\mathrm{I}=\frac{2\pi }{3}+\frac{\sqrt{3}}{2}$$

$$\mathrm{I}=-\frac{2\pi }{3}-\frac{\sqrt{3}}{2}$$

$$\mathrm{I}=-\frac{2\pi }{3}+\frac{\sqrt{3}}{2}$$

$$\mathrm{I}=60\frac{2}{7}$$

$$\mathrm{I}=66\frac{2}{7}$$

$$\mathrm{I}=-60\frac{2}{7}$$

$$\mathrm{I}=-66\frac{2}{7}$$

$$\mathrm{I}=\frac{2}{3}\mathrm{x}\sqrt{\mathrm{x}}+2\sqrt{\mathrm{x}}+\mathrm{C}$$

$$\mathrm{I}=\frac{1}{3}\mathrm{x}\sqrt{\mathrm{x}}+2\sqrt{\mathrm{x}}+\mathrm{C}$$

$$\mathrm{I}=\frac{2}{3}\mathrm{x}\sqrt{\mathrm{x}}+3\sqrt{\mathrm{x}}+\mathrm{C}$$

$$\mathrm{I}=\frac{2}{3}{\mathrm{x}}^2\sqrt{\mathrm{x}}+3\sqrt{\mathrm{x}}+\mathrm{C}$$

$$\mathrm{I}=\frac{1}{3}(2\mathrm{x}+1){\mathrm{e}}^{3x}-\frac{1}{9}{\mathrm{e}}^{3x}+\mathrm{C}$$

$$\mathrm{I}=\frac{1}{6}(2\mathrm{x}+1){\mathrm{e}}^{3x}-\frac{1}{3}{\mathrm{e}}^{3x}+\mathrm{C}$$

$$\mathrm{I}=\frac{1}{2}(2\mathrm{x}+1){\mathrm{e}}^{3x}-\frac{1}{9}{\mathrm{e}}^{3x}+\mathrm{C}$$

$$\mathrm{I}=\frac{1}{6}(2\mathrm{x}+1){\mathrm{e}}^{3x}-\frac{1}{9}{\mathrm{e}}^{3x}+\mathrm{C}$$

$$[-1;+\infty )$$

$$(1;+\infty )$$

$$[\frac{-1}{3};+\infty )$$

$$(-1;+\infty )$$

$$\frac{\mathrm{xsin}(\sqrt{1+{\mathrm{x}}^2})}{(\sqrt{1+{\mathrm{x}}^2})}$$

$$\frac{-\mathrm{x}\sin (\sqrt{1+{\mathrm{x}}^2})}{(\sqrt{1+{\mathrm{x}}^2})}$$

$$\frac{2xsin(\sqrt{1+{\mathrm{x}}^2})}{(\sqrt{1+{\mathrm{x}}^2})}$$

$$\frac{\mathrm{xcos}(\sqrt{1+{\mathrm{x}}^2})}{(\sqrt{1+{\mathrm{x}}^2})}$$

$\{\begin{array}{c}a=-\frac{1}{4}\\ b=\frac{13}{4}\end{array}$

$\{\begin{array}{c}a=-\frac{1}{4}\\ b=-\frac{13}{4}\end{array}$

$\{\begin{array}{c}a=-\frac{1}{4}\\ b=-\frac{3}{4}\end{array}$

$\{\begin{array}{c}a=\frac{1}{4}\\ b=-\frac{3}{4}\end{array}$

$$\sqrt{3}+\frac{\pi }{6}$$

$$\sqrt{3}-\frac{\pi }{6}$$

$$\frac{5\pi }{6}-\sqrt{3}$$

$$\pi -2$$

$$\mathrm{y}=\mathrm{C}\sqrt{1+{\mathrm{x}}^2}$$

$$\mathrm{y}=\mathrm{C}\sqrt{1+\mathrm{x}}$$

$$\mathrm{y}=-\mathrm{C}\sqrt{1+{\mathrm{x}}^2}$$

$$\mathrm{y}=-\mathrm{C}\sqrt{1+\mathrm{x}}$$

$$\ln \left|\frac{\mathrm{x}}{\mathrm{y}}\right|-\frac{1}{\mathrm{x}}-\frac{1}{\mathrm{y}}=\mathrm{C}$$

$$\ln \left|\frac{\mathrm{x}}{\mathrm{y}}\right|+\frac{1}{\mathrm{x}}-\frac{1}{\mathrm{y}}=\mathrm{C}$$

$$\ln \left|\frac{\mathrm{x}}{\mathrm{y}}\right|-\frac{1}{\mathrm{x}}+\frac{1}{\mathrm{y}}=\mathrm{C}$$

$$\ln \frac{\mathrm{x}}{\mathrm{y}}-\frac{1}{\mathrm{x}}-\frac{1}{\mathrm{y}}=\mathrm{C}$$

Ma trận của một hệ trực chuẩn trong cơ sở bất kỳ là một ma trận trực giao

Nếu A là ma trận trực giao thì At cũng là ma trận trực giao

Ma trận trực giao chỉ nhận các giá trị riêng là 1 hoặc 1 −

Nếu A, là hai ma tr B ận trực giao thì AB cũng là ma trận trực giao

$$\mathrm{x}=\frac{2}{3},\mathrm{y}=\frac{-1}{3},\mathrm{z}=\frac{1}{3}$$

$$\mathrm{x}=\frac{4}{3\sqrt{2}},\mathrm{y}=\frac{-1}{3\sqrt{2}},\mathrm{z}=\frac{-1}{3\sqrt{2}}$$

$$\mathrm{x}=\frac{-4}{3\sqrt{2}},\mathrm{y}=\frac{1}{3\sqrt{2}},\mathrm{z}=\frac{-1}{3\sqrt{2}}$$

$$\mathrm{x}=-4\sqrt{2},\mathrm{y}=\sqrt{2},\mathrm{z}=\sqrt{2}$$

Tự đồng cấu f là tự đồng cấu trực giao khi và chỉ khi ma trận của f một trong cơ sở trực chuẩn là ma trận trực giao

Tự đồng cấu f là tự đồng cấu đối xứng khi và chỉ khi ma trận của f một trong cơ sở trực chuẩn là ma trận đối xứng

Mọi ma trận đối xứng đều chéo hoá trực giao được

Ma trận đối xứng chỉ nhận các giá trị riêng khác 0

$$\mathrm{A}=\left(\begin{array}{ccc}\frac{1}{\sqrt{3}}& 0& \frac{2}{\sqrt{6}}\\ \frac{1}{\sqrt{3}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{6}}\\ 2& -1& 3\end{array}\right),{\mathrm{P}}^{-1}\mathrm{AP}=\left(\begin{array}{ccc}3& 0& 0\\ 0& 5& 0\\ 0& 0& 9\end{array}\right)$$

$$\mathrm{A}=\left(\begin{array}{ccc}\frac{-2}{\sqrt{6}}& 0& \frac{1}{\sqrt{3}}\\ \frac{1}{\sqrt{6}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{3}}\\ \frac{-1}{\sqrt{6}}& \frac{-1}{\sqrt{2}}& \frac{1}{\sqrt{3}}\end{array}\right),{\mathrm{P}}^{-1}\mathrm{AP}=\left(\begin{array}{ccc}-2& 0& 0\\ 0& 4& 0\\ 0& 0& 4\end{array}\right)$$

$$\mathrm{A}=\left(\begin{array}{ccc}\frac{1}{\sqrt{3}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{6}}\\ \frac{1}{\sqrt{3}}& \frac{-1}{\sqrt{2}}& \frac{1}{\sqrt{6}}\\ \frac{1}{\sqrt{3}}& 0& \frac{-2}{\sqrt{6}}\end{array}\right),{\mathrm{P}}^{-1}\mathrm{AP}=\left(\begin{array}{ccc}0& 0& 0\\ 0& 3& 0\\ 0& 0& 3\end{array}\right)$$

$$\mathrm{A}=\left(\begin{array}{ccc}\frac{1}{\sqrt{6}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{3}}\\ \frac{1}{\sqrt{6}}& \frac{-1}{\sqrt{2}}& \frac{1}{\sqrt{3}}\\ \frac{-2}{\sqrt{6}}& 0& \frac{1}{\sqrt{3}}\end{array}\right),{\mathrm{P}}^{-1}\mathrm{AP}=\left(\begin{array}{ccc}0& 0& 0\\ 0& 6& 0\\ 0& 0& 6\end{array}\right)$$

$$\mathrm{A}=\left(\begin{array}{ccc}\frac{1}{\sqrt{3}}& 0& \frac{2}{\sqrt{6}}\\ \frac{1}{\sqrt{3}}& \frac{1}{\sqrt{2}}& \frac{-1}{\sqrt{6}}\\ \frac{-1}{\sqrt{3}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{6}}\end{array}\right),{\mathrm{P}}^{-1}\mathrm{AP}=\left(\begin{array}{ccc}3& 0& 0\\ 0& 5& 0\\ 0& 0& 9\end{array}\right)$$

$$\mathrm{A}=\left(\begin{array}{ccc}\frac{-2}{\sqrt{6}}& 0& \frac{1}{\sqrt{3}}\\ \frac{1}{\sqrt{6}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{3}}\\ \frac{-1}{\sqrt{6}}& \frac{-1}{\sqrt{2}}& \frac{1}{\sqrt{3}}\end{array}\right),{\mathrm{P}}^{-1}\mathrm{AP}=\left(\begin{array}{ccc}-2& 0& 0\\ 0& 4& 0\\ 0& 0& 4\end{array}\right)$$

$$\mathrm{A}=\left(\begin{array}{ccc}\frac{1}{\sqrt{3}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{6}}\\ \frac{1}{\sqrt{3}}& \frac{-1}{\sqrt{2}}& \frac{1}{\sqrt{6}}\\ \frac{1}{\sqrt{3}}& 0& \frac{-2}{\sqrt{6}}\end{array}\right),{\mathrm{P}}^{-1}\mathrm{AP}=\left(\begin{array}{ccc}0& 0& 0\\ 0& 3& 0\\ 0& 0& 3\end{array}\right)$$

$$\mathrm{A}=\left(\begin{array}{ccc}\frac{1}{\sqrt{6}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{3}}\\ \frac{1}{\sqrt{6}}& \frac{-1}{\sqrt{2}}& \frac{1}{\sqrt{3}}\\ \frac{-2}{\sqrt{6}}& 0& \frac{1}{\sqrt{3}}\end{array}\right),{\mathrm{P}}^{-1}\mathrm{AP}=\left(\begin{array}{ccc}0& 0& 0\\ 0& 6& 0\\ 0& 0& 6\end{array}\right)$$

$$A=\left(\begin{array}{ccc}3& 2& -4\\ 2& 2& 2\\ -4& 2& -1\end{array}\right)$$

$$A=\left(\begin{array}{ccc}3& 2& -4\\ 0& 2& 2\\ 0& 0& -1\end{array}\right)$$

$$A=\left(\begin{array}{ccc}3& 2& -2\\ 1& 2& 1\\ -2& 1& -1\end{array}\right)$$

$$A=\left(\begin{array}{ccc}-3& 2& -4\\ 2& -2& 2\\ -4& 2& 1\end{array}\right)$$

$$\left(\begin{array}{cc}2& -3\\ -3& 1\end{array}\right)$$

$$\left(\begin{array}{cc}2& -1\\ -1& -3\end{array}\right)$$

$$\left(\begin{array}{cc}2& -6\\ -6& 1\end{array}\right)$$

$$\left(\begin{array}{cc}2& -6\\ 0& 1\end{array}\right)$$

p = 1, q = 2

p = 2, q = 1

p = 1, q = 1

p = 0, q = 2

p = 1, q = 3

p = 3, q = 1

p = 2, q = 2

p = 1, q = 2