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We investigate analytically a large-scale coherence in the orientation ofgalaxies embedded in two-dimensional sheet-like structures in the frame of thetidal torque theory. Assuming that the galaxy spin and the surrounding matterfields are intrinsically aligned in accordance with the tidal torque model, wefirst derive analytically the probability distribution of the galaxy positionangles, and evaluate the degree of their inclinations relative to the plane ofthe sheet. Then, we apply our analytic approach to the nearby spirals in theLocal Super Cluster, and provide theoretical explanations about why and to whatdegree the nearby spirals are inclined relative to the supergalatic plane.Finally, we conclude that the observed large-scale coherence in the orientationof nearby spirals relative to the supergalactic plane can be quantitativelyunderstood in terms of galaxy intrinsic alignment predicted by the tidal torquetheory, and that the spins of luminous galaxies might be more strongly alignedwith the surrounding matter than the underlying dark halos. If applied to largescale surveys like Sloan Digital Sky Survey (SDSS), our analytic approach willallow us to measure accurately the strength of galaxy intrinsic alignment whichplays a role of statistical error in weak lensing searches and can be used as afossil record to reconstruct cosmology.Comment: accepted by the ApJ Letters, revised version, typos and mistakes  corrected,12 pages, 3 figure

The Intrinsic Inclination of Galaxies Embedded in Cosmic Sheets and Its Cosmological Implications: An Analytic Calculation