Place pork tenderloin on a rack in a shallow roasting pan. Insert a meat thermometer. Roast in a 425 degree F oven for 25 to 35 minutes or until thermometer registers 160 degrees F.
Meanwhile, in a large saucepan combine cabbage, onion, carrots, water, vinegar, dillweed, salt, and pepper. Bring to boiling; reduce heat. Cover and simmer for 8 to 10 minutes or until vegetables are just tender.
Slice pork and serve with vegetables. Makes 4 servings.