A. Only God can be worshipped. But we can revere Mary as the Mother of our Lord. 
By worship we mean the humble, unconditional acknowledgment of the absolute superiority of God over all creatures. Mary is a creature like us. In faith she is our Mother. And we should honor our parents. There is a biblical basis for this, since Mary herself says, “For behold, henceforth all generations will call me blessed” (Lk 1:48b). So the Church has Marian shrines and places of pilgrimage, feast days, hymns, and prayers, for instance, the Rosary. It is a compendium of the Gospel.