# Recent questions tagged clockwise

Suppose $S$ is a piecewise smooth surface which forms the complete boundary of a bounded closed point set $V$, and $S$ is oriented by its normal being outwards from $V$. ThenSuppose $S$ is a piecewise smooth surface which forms the complete boundary of a bounded closed point set $V$, and $S$ is oriented by its normal ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Suppose $S$ is an oriented surface with boundary $\partial S$ which is oriented so that its direction is clockwise relative to the normals of $S$. Then
Suppose $S$ is an oriented surface with boundary $\partial S$ which is oriented so that its direction is clockwise relative to the normals of $S$. ThenSuppose $S$ is an oriented surface with boundary $\partial S$ which is oriented so that its direction is clockwise relative to the normals of $S\ ... close 0 answers 44 views Linear maps \(F(X)=A X$, where $A$ is a matrix, have the property that $F(0)=A 0=0$, so they necessarily leave the origin fixed. It is simple to extend this to include a translation, Linear maps $F(X)=A X$, where $A$ is a matrix, have the property that $F(0)=A 0=0$, so they necessarily leave the origin fixed. It is simple t ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Find a real $2 \times 2$ matrix $A$ (other than $A=I$ ) such that $A^{5}=I$.
Find a real $2 \times 2$ matrix $A$ (other than $A=I$ ) such that $A^{5}=I$.Find a real $2 \times 2$ matrix $A$ (other than $A=I$ ) such that $A^{5}=I$. ...
close
Find a $3 \times 3$ matrix $A$ mapping $\mathbb{R}^{3} \rightarrow \mathbb{R}^{3}$ that rotates the $x_{1} x_{3}$ plane by 60 degrees and leaves the $x_{2}$ axis fixed.Find a $3 \times 3$ matrix $A$ mapping $\mathbb{R}^{3} \rightarrow \mathbb{R}^{3}$ that rotates the $x_{1} x_{3}$ plane by 60 degrees and leav ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Find a $3 \times 3$ matrix that acts on $\mathbb{R}^{3}$ as follows: it keeps the $x_{1}$ axis fixed but rotates the $x_{2} x_{3}$ plane by 60 degrees.
Find a $3 \times 3$ matrix that acts on $\mathbb{R}^{3}$ as follows: it keeps the $x_{1}$ axis fixed but rotates the $x_{2} x_{3}$ plane by 60 degrees.Find a $3 \times 3$ matrix that acts on $\mathbb{R}^{3}$ as follows: it keeps the $x_{1}$ axis fixed but rotates the $x_{2} x_{3}$ plane by 60 ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Find a matrix that rotates the plane through $+60$ degrees, keeping the origin fixed.
Find a matrix that rotates the plane through $+60$ degrees, keeping the origin fixed.Find a matrix that rotates the plane through $+60$ degrees, keeping the origin fixed. ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees followed by a reflection across the horizontal axis.
Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees followed by a reflection across the horizontal axis.Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees followed by a reflection across the horizontal axis. ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees $(+45$ degrees means 45 degrees counterclockwise).
Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees $(+45$ degrees means 45 degrees counterclockwise).Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees $(+45$ degrees means 45 degrees counterclockwise). ...