oxygen in water carries a partial negative charge, and hydrogen carries a corresponding partial positive charge making water a polar molecule?

Yes, that is correct. Water is a polar molecule because of its bent molecular shape and the unequal distribution of electrons between the oxygen and hydrogen atoms. The oxygen atom is more electronegative than the hydrogen atoms, so it attracts the shared electrons more strongly, giving it a partial negative charge (δ-) and the hydrogen atoms a partial positive charge (δ+).

Yes, that's correct. Water is a polar molecule because the oxygen atom has a higher electronegativity than the hydrogen atoms. Electronegativity is the ability of an atom to attract electrons towards itself in a covalent bond. In the water molecule, the oxygen atom pulls the shared electrons closer to itself, creating a partial negative charge (δ-) on the oxygen atom and a partial positive charge (δ+) on the hydrogen atoms. This uneven distribution of charge creates a dipole moment, making water a polar molecule.