$$ W = \vecF \cdot \vecd $$ $$ W = (3\hati + 4\hatj) \cdot (3\hati + 4\hatj) $$ $$ W = (3 \times 3) + (4 \times 4) $$ $$ W = 9 + 16 = 25 \text Joules $$

Each solution should read like a short proof a user manual for the physical system.

Compute: ( \mathbfX^T \mathbfX = \beginbmatrix3 & 6 \ 6 & 14\endbmatrix, \quad \mathbfX^T \mathbfy = \beginbmatrix11.8 \ 26.3\endbmatrix ).

Differential equations are the backbone of modelling change over time (population growth, cooling, circuits).

Modern search engines and social media algorithms are essentially massive applied math problems centered on linear algebra and graph theory.