Answer true or false to the following statement and explain your answer. Any

The following are each a result of a single transformation. What type of transformation occurred for image E.

Give the correct answer and solve the given equation $V=T(m,n),$
The set of lineartrans formations
$T:R^m\to R^n,$
together with the usualadditionand scalar multiplication of functions.

To state:
The solution of the given initial value problem using the method of Laplace transforms.
Given:
The initial value problem is,
$y+6y^{\prime }+5y=12e^t,y\left(0\right)=-1,y^{\prime }\left(0\right)=7$

Determine whether the following series converge or diverge using the properties.
${\displaystyle \sum _{k=0}^{\mathrm{\infty }}\frac{10}{k^2+9}}$

The given initial-value problem.
$y^{″}-2y^{\prime }-8y=5$
$y(0)=1$
$y^{\prime }(0)=0$

Which of the following are linear transformations from $R{R}^2\to R{R}^2?$
(d) Rotation: if $x=r\cos \theta ,y=r\sin \theta ,$ then
$\overrightarrow{T}(x,y)=(r\cos (\theta +\phi ),r\sin (\theta +\phi ))$
for some constants $\mathrm{\angle }\phi$
(f) Reflection: given a fixed vector $\overrightarrow{r}=(a,b),\overrightarrow{T}$ maps each point to its reflection with
respect to $\overrightarrow{r}\overrightarrow{T}(\overrightarrow{x})=\overrightarrow{x}-2{\overrightarrow{x}}_{r\perp }$
$=2{\overrightarrow{x}}_r-\overrightarrow{x}$