Please i need help for this for $w\in W^{1,p}(\mathbb{R}^N)$, we define $w_R(x)=h_{R}(x)w(x)$

where $h\in C_0^{\infty}(\mathbb{R}^N,[0,1]), h(x)=1,~ x\in B_1(0)$ and $h(x)=0,~ x\in B^c_2(0)$ and $R>0$ , $h_{R}(x)=h(\frac{x}{R})$

How to show that

$$\lim_{n\to\infty}\int_{\mathbb{R}^N}(|\nabla w_{R_n}|^p+|w_{R_n}|^p)dx=\int_{\mathbb{R}^N}(|\nabla w|^p+|w|^p)dx$$

with $(R_n)$ is a real sequence such that $R_{n}\to \infty$ when $n\to\infty$.

Hey ! Could someone give me a hand here ?
Given $V$ and $W$ subspaces.
How can I create a linear transformation $T: R^4$ such that $Ke(T) = V$ and $Im(T) = W$ ?

Give the coordinates of $T$ respect to $\{T_1,T_2,T_3,T_4\}$
Where

$T_1(x,y) = (x,x)$
$T_2(x,y) = (y,y)$
$T_3(x,y) = (-x,y)$
$T_4(x,y) = (x,y)$

Basically
$ ax + by -cx +dx = y $
$ ax + by +cy +dy = x $

$\begin{bmatrix}
x & y & -x & x & y \\
x & y & y & y & x
\end{bmatrix}$