Heat olive oil in a medium size skillet on medium-high heat. Add onion, anchovies and garlic. Saute until onion is clear, about 5 minutes. Raise the heat to high and add vodka. Boil until reduced by half, about 1 minute.
Lower heat to medium. Add the tomatoes. Cover with a lid and cook gently without boiling for about 2 minutes.
Add the shrimp, cover and cook 3 more minutes. Add the cream, stir and add salt and pepper to taste.
Place linguine in boiling water and boil according to package. Drain, and toss with sauce.