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Can you translate “miete rucke”, the sentence is translated below:
“take a seat”, “sit down”

A:

‘sit’ is a contraction of’sit’ and that is the meaning of the sentence.
And no, Google Translate does not work as well with words of German origin as it works with words of French origin. You should be aware of that when you use it.

Risk assessment and appraisal of benefit of environmental impact studies on water management in a tropical seasonal rainforest.
In an attempt to understand the importance of water quality in ecosystem function and how the different impacts of environmental impact on water quality can be identified and avoided, we used a semi-quantitative risk approach and the Water Framework Directive (WFD) framework to explore the potential impact of wetland management activities in a tropical rainforest. Our results indicated that potential impacts may arise from different restoration projects using different combinations of activities. For example, we found that restoration activities that focus solely on re-establishing water to the system and neglect control of sediment, nutrients or pesticide loadings, could have impacts on water quality, even if the cumulative risk value, defined as the potential risk of impacts, was low. Under the WFD, the true risk value is the potential contribution of the intervention to reduce the current or an increased frequency of adverse effects or non-compliance. Thus, our study may assist in the re-assessment of some projects by providing a case study and providing an example of the approaches needed to conduct such analysis in tropical ecosystems.Q:

Inequality for order of a product of matrices

Let $T$ be an invertible $n\times n$ matrix and $H,K$ be $m\times n$ matrices, then I have to prove that if $H^T H=K^T K$, then
$$(T^{ -1}H^T K T^{ -1})^T(T^{ -1}H^T K T^{ -1})= \frac{1}{\text{det }T}(H^T K H)^T(H^T K H)$$
I’ve done following:
let $C=T^{ -1}H^T K T^{ -1}$, thus $C^T C=I$. Since $C$ is invertible, it follows that $C^T=I$, thus \$
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