This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
\begin{pmatrix} 14 \ 5 \end{pmatrix}
Hapa kuna suluhisho la swali la 15(a):
Swali la 15(a): Tafsiri T inahamisha nukta hadi . Tafuta wapi T inahamisha nukta .
Step 1: Tafuta vekta ya tafsiri. Tafsiri T inahamisha nukta hadi . Hii inamaanisha kuwa mabadiliko katika x ni . Na mabadiliko katika y ni . Kwa hiyo, vekta ya tafsiri ni .
Step 2: Tumia vekta ya tafsiri kwa nukta . Ili kupata wapi T inahamisha nukta , ongeza vekta ya tafsiri kwa nukta hii: Kwa hivyo, T inahamisha nukta hadi .
Jibu la mwisho ni: \begin{pmatrix 14 \\ 5 \end{pmatrix}}
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Hapa kuna suluhisho la swali la 15(a): Swali la 15(a): Tafsiri T inahamisha nukta (-3,2) hadi (4,3).
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.