In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. Since the legs are a and b and the hypotenuse is c, the relationship is c^2 = a^2 + b^2. This is the exact equation that matches the Pythagorean theorem for these side lengths. The other forms would imply a different hypotenuse or come from a different identity, and c^2 = a^2 + b^2 is the straightforward expression of the right-triangle relationship.

Harriet Beecher Stowe is the author. Uncle Tom's Cabin, published in 1852, is a landmark anti-slavery novel written by her, and its vivid portrayal of enslaved people’ lives helped galvanize the abolitionist movement in the United States. The author became closely associated with this work and its impact on American history. Other well-known authors wrote different works—Nathaniel Hawthorne authored The Scarlet Letter, Mark Twain wrote Tom Sawyer and Huckleberry Finn, and Virginia Woolf wrote novels like Mrs. Dalloway—so they are not the creators of this particular book.

Pilosopo Tasyo acts as the voice of the educated Filipino thinker who observes society with a mix of humor and critique. In some interpretations, this persona is understood to be based on a real person named Simon who existed in Rizal’s circle, embodying the traits Tasyo displays—a worldly, bookish man capable of lofty ideas that clash with common beliefs. The idea isn’t that Rizal himself is Tasyo; rather, Rizal uses Tasyo to give a face to the kind of intellectual who challenges tradition and points out social flaws. That connection to a real-life Simon is why this answer fits best. The other options don’t align since Isagani is a separate character, and Rizal as the author or Pilosopo Tasyo himself wouldn’t be described as being personified by someone else in reality.

Osmosis is the movement of water across a semipermeable membrane down its water potential gradient. Water potential reflects how freely water molecules can move: it’s higher where there is more free water (less solute) and lower where solute concentration is higher or where pressure constrains water movement. Because water tends to move toward lower water potential, it flows from regions of high water potential to regions of low water potential through the membrane. That means the statement describing water moving from high to low water potential is describing the actual direction of osmotic flow. Osmosis is a passive process, requiring no external energy input, and it proceeds along the gradient until equilibrium is reached or balanced by opposing pressures. The other ideas—water moving from low to high water potential, requiring energy, or moving equally in all SAMPLEdirections regardless of gradient—do not reflect how osmosis operates.