Is there any relationship between the following two expectations?

Question

Is there any relationship between the following two expectations?

1. $\mathbb{E}_{\mathbb{Q}}[\|\boldsymbol{\tilde{\xi}} - \boldsymbol{\tilde{\xi}}^{\prime}\|]$, and
2. $\mathbb{E}_{\mathbb{Q}}[\|\mathbf{A}(\boldsymbol{\tilde{\xi}} - \boldsymbol{\tilde{\xi}}^{\prime})\|]$.

Here, $\mathbb{Q}$ is the joint distribution of $\boldsymbol{\tilde{\xi}}$ and $\boldsymbol{\tilde{\xi}}^{\prime}$ and $\mathbf{A}$ is a general matrix. If it is possible, is there an equality relationship?

Actually, I am considering the relationship between two Wasserstein metrics: $d_{\mathrm{W}}\Big(\mathbb{P}_{\boldsymbol{\tilde{\xi}}}, \widehat{\mathbb{P}}_{\boldsymbol{\tilde{\xi}}}\Big)$ and $d_{\mathrm{W}}\Big(\mathbb{P}_{\mathbf{A}\boldsymbol{\tilde{\xi}}}, \widehat{\mathbb{P}}_{\mathbf{A}\boldsymbol{\tilde{\xi}}}\Big)$. I guess the above direction may be helpful.