Why do we feel hotter from the metal than the wood when we place them in the boiling hot water?
The metal has a much stronger specific heat (or heat capacity) and thermal conductivity than the wood.
What core concepts in Calculus use most often to solve real world problems?
Derivatives and Integrals are the most important concepts for real world Calculus. The most known example is our coffee machine, which uses PID controller that are made from calculating the integrals between input and output of a machine.
What components make up the "dark matter"?
All of our visible substances only constitute roughly 4% of the whole universe. The Big Bang emitted both visible and invisible elements. We learned from Physics class that matter is made of atoms, and atoms contain both protons and neutrons, with electrons on the outermost energy shell to balance with the charge of protons inside the nucleus so atoms are neutral. However, besides atoms there are also invisible matters which are also electrically neutral, and can not absorb or reflect light from the sun which make them to called the "dark matter".