Contribution of this paper is a proposal of the new special type of telescope with a parabolic strip as a primary element for astronomical observations or for measurements with good angular resolution in one direction. The observed objects are displayed as lines in the image plane of a length equal to the width of the mirror strip. If we observe a sufficiently bright object, the observation allows us to distinguish fine detail or fine movements on the sky. Each line segment corresponds to the integral intensity of the incident light from the observed object in the direction perpendicular to the mirror strip. For the reconstruction of the whole image with good resolution we need a parabolic mirror strip to rotate around the optical axis, and a series of sequential snaps with a special camera. Different algorithms for reconstruction of the image are used. The main advantage of this rotating telescope is mechanical and manufacturing technological simplicity and an innovative design. Nothing comparable has yet been made. Currently constructed large telescopes are made up of segments, using adaptive optics, and generally it is technologically challenging. Systems of interfering telescopes are built (the effective diameter of 30 m to the get better resolution. The proposed telescope can be made of a 50-m long tape without any technological problems. We created two prototypes of telescopes: a small one, with a 0.3-m long mirror strip, and a bigger one, with a 1.4-m long mirror strip. Both telescopes are supported by parallactic mountings, and both are equipped with special cameras with optics, electronics, computer with special controlling software, special servo stepper motors fitted with mechanical transmission, construction of lightweight alloys, plastics and composites.